Class 7 Maths Worksheet: Algebraic Expressions - Addition & Subtraction

Let’s solve each problem step by step. We’ll go one at a time, carefully combining like terms and watching signs.

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1. Add (7j³ - 2) + (5j³ - j - 3)

Combine like terms:

- j³ terms: 7j³ + 5j³ = 12j³
- j term: only -j → -j
- constants: -2 + (-3) = -5

→ Answer: 12j³ - j - 5

✔ Matches option: 12j³ - j - 5

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2. Add (-5x² - x + 4) + (-3x² - 5x + 2)

Combine like terms:

- x² terms: -5x² + (-3x²) = -8x²
- x terms: -x + (-5x) = -6x
- constants: 4 + 2 = 6

→ Answer: -8x² - 6x + 6

*(Note: This question doesn’t give options — so we just write the simplified expression.)*

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3. Subtract 13x + 12y - 5 from 27x + 5y - 43

That means:
(27x + 5y - 43) - (13x + 12y - 5)

Distribute the minus sign:

= 27x + 5y - 43 - 13x - 12y + 5

Now combine:

- x: 27x - 13x = 14x
- y: 5y - 12y = -7y
- constants: -43 + 5 = -38

→ Answer: 14x - 7y - 38

✔ Matches option: 14x - 7y - 38

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4. Simplify (x+y-z) + (3x-5y+7z) - (14x+7y-6z)

First, remove parentheses (watch the minus on the last group):

= x + y - z + 3x - 5y + 7z - 14x - 7y + 6z

Now combine like terms:

- x: x + 3x - 14x = -10x
- y: y - 5y - 7y = -11y
- z: -z + 7z + 6z = 12z

→ Answer: -10x - 11y + 12z

*(No options given — this is the simplified form.)*

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5. Find x² - [3x + [2x - (x² - 1)] + 2]

Work from inside out.

Start with innermost: (x² - 1) → stays as is for now.

Then: 2x - (x² - 1) = 2x - x² + 1

Now plug into next bracket:
3x + [2x - x² + 1] + 2 = 3x + 2x - x² + 1 + 2 = 5x - x² + 3

Now whole expression:
x² - [5x - x² + 3] = x² - 5x + x² - 3

Combine:
x² + x² = 2x²
-5x
-3

→ Answer: 2x² - 5x - 3

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6. Solve for n + (m + 1) + (n + 2) + (m + 3) + (n + 4) + (m + 5)

Remove parentheses:

= n + m + 1 + n + 2 + m + 3 + n + 4 + m + 5

Group like terms:

- m: m + m + m = 3m
- n: n + n + n = 3n
- constants: 1+2+3+4+5 = 15

→ Answer: 3m + 3n + 15

✔ Matches option: 3m + 3n + 15

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7. Subtract 3x² - 6x - 4 from 5 + x - 2x²

Means: (5 + x - 2x²) - (3x² - 6x - 4)

Distribute minus:

= 5 + x - 2x² - 3x² + 6x + 4

Combine:

- x²: -2x² - 3x² = -5x²
- x: x + 6x = 7x
- constants: 5 + 4 = 9

→ Answer: -5x² + 7x + 9

*(Drag and drop — match to correct box later if needed.)*

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8. Add 7abc, -5abc, 9abc and -8abc

All are like terms (same variables).

Add coefficients: 7 - 5 + 9 - 8 = (7+9) + (-5-8) = 16 - 13 = 3

→ Answer: 3abc

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9. Add 2x²–3x+1 to the sum of 3x²–2x and 3x+7

First, find sum of 3x²–2x and 3x+7:

= 3x² - 2x + 3x + 7 = 3x² + x + 7

Now add 2x² – 3x + 1 to that:

= (3x² + x + 7) + (2x² - 3x + 1)

Combine:

- x²: 3x² + 2x² = 5x²
- x: x - 3x = -2x
- constants: 7 + 1 = 8

→ Answer: 5x² - 2x + 8

Wait — let me double-check:

Original: “Add 2x²–3x+1 to the sum of 3x²–2x and 3x+7”

Sum of 3x²–2x and 3x+7:
3x² + (-2x + 3x) + 7 = 3x² + x + 7 ✔️

Add 2x² - 3x + 1:
3x² + 2x² = 5x²
x - 3x = -2x
7 + 1 = 8

Yes → 5x² - 2x + 8

But looking at the drag-and-drop options at bottom, none say exactly that? Wait — maybe I misread.

Wait — in the image, under Q10, there are boxes including “5x² + 2x + 8” — but that’s not what we got.

Hold on — perhaps I made a mistake?

Wait — let’s re-read Q9:

“Add 2x²–3x+1 to the sum of 3x²–2x and 3x+7.”

Sum of 3x²–2x and 3x+7:

3x² - 2x + 3x + 7 = 3x² + x + 7 ✔️

Now add 2x² - 3x + 1:

So total: 3x² + x + 7 + 2x² - 3x + 1

x terms: x - 3x = -2x → yes.

But maybe the question meant something else? Or perhaps the answer isn't among the bottom boxes? Actually, Q9 has its own blank — no options shown directly under it. The bottom boxes seem to be for Q7, Q8, Q10.

Looking back: Q7, Q8, Q9, Q10 all have blanks, then below them are four boxes labeled:

- 4x-y-2z+7
- 3abc
- -5x² + 7x + 9
- 5x² + 2x + 8

Ah! So those are likely answers for Q7, Q8, Q10 — and maybe Q9 is separate? But Q9 should be 5x² - 2x + 8 — which is NOT listed. Hmm.

Wait — did I misread Q9?

“Add 2x²–3x+1 to the sum of 3x²–2x and 3x+7.”

Perhaps “sum of 3x²–2x and 3x+7” is interpreted differently? No, standard interpretation is correct.

Alternatively — maybe typo in my calculation? Let's do again:

Sum: (3x² - 2x) + (3x + 7) = 3x² + (-2x + 3x) + 7 = 3x² + x + 7

Add (2x² - 3x + 1):
3x² + 2x² = 5x²
x - 3x = -2x
7 + 1 = 8

Still 5x² - 2x + 8.

But since it’s not in the options, and the instruction says “drag and drop”, perhaps for Q9 we leave it as is, or maybe I need to check if any option matches.

Wait — look at the last box: “5x² + 2x + 8” — close but sign wrong on x term.

Unless... did I misread the original expressions?

Q9: “Add 2x²–3x+1 to the sum of 3x²–2x and 3x+7.”

What if “3x²–2x” is 3x² minus 2x, and “3x+7” is plus — yes.

Perhaps the problem is that when adding, someone might forget to distribute correctly — but I think my math is right.

Maybe the intended answer is different? Let me try another way.

Total expression: (2x² - 3x + 1) + [(3x² - 2x) + (3x + 7)]

= 2x² - 3x + 1 + 3x² - 2x + 3x + 7

Now combine all:

x²: 2x² + 3x² = 5x²

x: -3x -2x + 3x = (-5x + 3x) = -2x

constants: 1 + 7 = 8

Same result.

So unless there’s a typo in the worksheet, the answer is 5x² - 2x + 8.

But since it’s not in the provided boxes, and the boxes are probably for other questions, I’ll proceed.

For now, we’ll note the answer as 5x² - 2x + 8

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10. Subtract -x²-3z from 5x²-y+z+7

Means: (5x² - y + z + 7) - (-x² - 3z)

Distribute the minus:

= 5x² - y + z + 7 + x² + 3z

Combine:

- x²: 5x² + x² = 6x²
- y: -y
- z: z + 3z = 4z
- constant: 7

→ Answer: 6x² - y + 4z + 7

Wait — but looking at the drag-and-drop options, one is “4x - y - 2z + 7” — not matching.

Another is “5x² + 2x + 8” — no.

Did I misread?

“Subtract -x²-3z from 5x²-y+z+7”

So: minuend is 5x² - y + z + 7
subtrahend is -x² - 3z

So: (5x² - y + z + 7) - (-x² - 3z) = 5x² - y + z + 7 + x² + 3z = 6x² - y + 4z + 7

But none of the bottom boxes match this.

Bottom boxes are:

- 4x-y-2z+7
- 3abc
- -5x² + 7x + 9
- 5x² + 2x + 8

None have 6x² or 4z.

Perhaps I misread the question.

Look back: “Subtract -x²-3z from 5x²-y+z+7”

Maybe it’s “subtract (-x² - 3z)” — which is what I did.

Or perhaps it’s “subtract -x² - 3z” meaning subtract each term — same thing.

Another possibility: maybe the expression is 5x² - y + z + 7, and we subtract (-x² - 3z), so yes.

But let’s check if any option could be for this.

Option “4x - y - 2z + 7” — has x not x², and negative z.

Not matching.

Perhaps I made a mistake in sign.

When you subtract a negative, it becomes positive.

So - (-x²) = +x²
- (-3z) = +3z

Yes.

So 5x² + x² = 6x²
z + 3z = 4z
-y and +7 remain.

So 6x² - y + 4z + 7

But since it’s not in options, and the worksheet might have typos, or perhaps I need to see which box corresponds.

Wait — maybe for Q10, the answer is not among those, or perhaps I misidentified.

Another thought: in Q10, it says “Subtract -x²-3z from 5x²-y+z+7”

Perhaps “-x²-3z” is meant to be -(x²) - 3z, which is what I took.

Maybe it’s - (x² - 3z)? But no, it’s written as "-x²-3z", which is -x² minus 3z.

I think my calculation is correct.

But let’s look at the very first part — for Q3, we had an option “14x - 7y - 38” which matched.

For Q1, “12j³ - j - 5” matched.

For Q6, “3m + 3n + 15” matched.

For Q7, we got “-5x² + 7x + 9” — which is one of the bottom boxes.

For Q8, “3abc” — also a bottom box.

For Q10, perhaps they expect us to choose from the boxes, but none match 6x² - y + 4z + 7.

Unless... did I misread the minuend?

“5x²-y+z+7” — is that 5x² minus y plus z plus 7? Yes.

Subtract “-x²-3z” — which is -x² minus 3z.

So subtraction: (5x² - y + z + 7) - (-x² - 3z) = 5x² - y + z + 7 + x² + 3z = 6x² - y + 4z + 7

Perhaps the answer is not listed, or maybe in the context, we select the closest, but that doesn't make sense.

Another idea: perhaps "Subtract -x²-3z" means subtract the quantity (-x² - 3z), which is what I did.

Maybe the expression is 5x² - (y + z + 7) or something, but no, it's written as "5x²-y+z+7", which typically means 5x² minus y plus z plus 7.

In algebra, without parentheses, it's left to right, but usually, we assume it's 5x² + (-y) + z + 7.

I think it's correct.

Perhaps for Q10, the intended answer is different, or there's a typo.

Let me calculate numerically to verify.

Suppose x=1, y=1, z=1

Minuend: 5(1)^2 -1 +1 +7 = 5 -1 +1 +7 = 12

Subtrahend: - (1)^2 -3(1) = -1 -3 = -4

Subtract: 12 - (-4) = 12 +4 = 16

Now my answer: 6(1)^2 -1 +4(1) +7 = 6 -1 +4 +7 = 16 ✔️

Now check the options:

- 4x-y-2z+7 = 4-1-2+7=8 ≠16

- 3abc — not applicable

- -5x²+7x+9 = -5+7+9=11≠16

- 5x²+2x+8=5+2+8=15≠16

None give 16. So either the worksheet has a mistake, or I misread the question.

Look back at the image description: "10. Subtract -x²-3z from 5x²-y+z+7"

Perhaps it's "Subtract (-x² - 3z)" — same thing.

Another possibility: maybe "from" is misinterpreted. In English, "subtract A from B" means B - A.

Yes, I did that.

Perhaps the expression is 5x² - (y + z + 7), but that would be unusual notation.

If it were 5x² - (y + z + 7) = 5x² - y - z - 7

Then subtract (-x² - 3z) = 5x² - y - z - 7 + x² + 3z = 6x² - y + 2z - 7

Still not matching.

Or if minuend is 5x² - y + z + 7, and we subtract -x² - 3z, same as before.

Perhaps the subtrahend is - (x² - 3z) = -x² + 3z, but the text says "-x²-3z", which is -x² minus 3z.

I think there might be a typo in the worksheet or in the options.

But for the sake of completing, and since the other answers match, perhaps for Q10, we'll go with our calculation.

However, looking at the bottom boxes, one is "4x - y - 2z + 7" — which has x instead of x², so probably not.

Another thought: in Q10, it might be "Subtract -x - 3z" not "-x²", but the text says "-x²".

In the user's message, it's "Subtract -x²-3z from 5x²-y+z+7" — so x squared.

Perhaps in the original image, it's different, but based on text, I'll stick with 6x² - y + 4z + 7.

But since the instruction is to provide final answer, and for drag and drop, perhaps for Q10, it's not among the options, but let's see the very end.

The user said: "Drag and drop the correct answer from the options given." and then lists Q7 to Q10 with blanks, and then four boxes.

Probably, the four boxes are for Q7, Q8, Q10, and perhaps Q9 or something.

From earlier:

Q7: -5x² + 7x + 9 — matches one box

Q8: 3abc — matches another box

Q10: should be 6x² - y + 4z + 7 — not matching

Q9: 5x² - 2x + 8 — not matching

But there is "5x² + 2x + 8" — close to Q9 but sign wrong.

Perhaps for Q9, if I miscalculated.

Let me double-check Q9.

"Add 2x²–3x+1 to the sum of 3x²–2x and 3x+7."

Sum of 3x²–2x and 3x+7: 3x² + (-2x + 3x) + 7 = 3x² + x + 7

Add 2x² - 3x + 1: 3x² + 2x² = 5x²; x - 3x = -2x; 7+1=8 → 5x² - 2x + 8

But if the sum was of 3x² - 2x and 3x + 7, and then add 2x² - 3x + 1, yes.

Perhaps "the sum of 3x²–2x and 3x+7" is 3x² - 2x + 3x + 7 = 3x² + x + 7, same.

Another idea: perhaps "add 2x²–3x+1 to the sum" means (sum) + (2x²–3x+1), which is what I did.

Maybe the expression is different.

Let's calculate numerical value for Q9.

Let x=1

Sum of 3(1)^2 -2(1) = 3-2=1, and 3(1)+7=10, sum=1+10=11

Add 2(1)^2 -3(1) +1 = 2-3+1=0

Total 11+0=11

My answer: 5(1)^2 -2(1) +8 = 5-2+8=11 ✔️

Now, if I take "5x² +2x +8" =5+2+8=15≠11

So not that.

Perhaps for Q10, if I use x=1,y=1,z=1, we had 16, and no option gives 16.

Unless "4x - y -2z +7" with x=1,y=1,z=1: 4-1-2+7=8≠16

"-5x²+7x+9" = -5+7+9=11≠16

"5x²+2x+8"=5+2+8=15≠16

"3abc" not applicable.

So perhaps there's a mistake in the worksheet, or in my reading.

Let's look back at the user's input for Q10: "10. Subtract -x²-3z from 5x²-y+z+7"

Perhaps it's "Subtract (-x^2 - 3z)" , same.

Another possibility: "from 5x² - y + z + 7" might be 5x² - (y + z + 7), but that would be unusual.

Assume that: 5x² - (y + z + 7) = 5x² - y - z - 7

Then subtract (-x² - 3z) = 5x² - y - z - 7 + x² + 3z = 6x² - y + 2z - 7

With x=1,y=1,z=1: 6-1+2-7=0, but earlier calculation gave 16, so not.

Perhaps the subtrahend is - (x² - 3z) = -x² + 3z

Then (5x² - y + z + 7) - (-x² + 3z) = 5x² - y + z + 7 + x² - 3z = 6x² - y -2z +7

With x=1,y=1,z=1: 6-1-2+7=10≠16

Still not 16.

Earlier when I calculated with actual values, minuend 5(1)^2 -1 +1 +7 = 5-1+1+7=12

Subtrahend - (1)^2 -3(1) = -1-3= -4

12 - (-4) = 16

So to get 16, and if I take "6x² - y + 4z + 7" =6-1+4+7=16, correct.

Perhaps the answer is not among the boxes, or for Q10, it's a different question.

Maybe "Subtract -x²-3z" means subtract the expression, but perhaps it's -x^2 - 3z, and in the context, they want us to simplify, but still.

Another idea: perhaps in Q10, "5x²-y+z+7" is 5x² - y + z + 7, and " -x²-3z" is to be subtracted, so yes.

I think for the purpose of this, I'll provide the correct mathematical answer, and for the drag and drop, perhaps the student can see.

But since the user asked to solve, I'll list all answers.

For the final answer section, since it's multiple questions, I need to provide all.

Perhaps the "Final Answer" is for the entire set, but that doesn't make sense.

Looking at the response format, it says "Final Answer: [Provide only the final correct answer]" — but for multiple problems, probably list them.

Perhaps for each question, but the format suggests one final answer.

This is ambiguous.

Perhaps in the context, since some have options, and some don't, but for the ones with options, we select, for others, write the expression.

But for the response, I think I should provide the answers to all 10 questions.

And for the drag and drop, identify which box goes where.

From above:

Q7: -5x² + 7x + 9 — matches the third box

Q8: 3abc — matches the second box

Q10: 6x² - y + 4z + 7 — not matching any, but perhaps it's a typo, and it's supposed to be something else.

Let's look at the first option: "4x - y -2z +7" — if it were 4x², but it's 4x.

Perhaps for Q10, if it was "Subtract -x -3z" not "-x²", then:

(5x² - y + z + 7) - (-x -3z) = 5x² - y + z + 7 + x + 3z = 5x² + x - y + 4z + 7 — still not matching.

If minuend is 5x - y + z + 7, then (5x - y + z + 7) - (-x² -3z) = 5x - y + z + 7 + x² + 3z = x² + 5x - y + 4z + 7 — not matching.

Perhaps "Subtract -x²-3z from 5x - y + z + 7" — then 5x - y + z + 7 + x² + 3z = x² + 5x - y + 4z + 7

Still not "4x - y -2z +7".

Another possibility: for Q10, "Subtract -x²-3z from 5x²-y+z+7" but perhaps " -x²-3z" is - (x² - 3z) = -x² + 3z, then (5x² - y + z + 7) - (-x² + 3z) = 5x² - y + z + 7 + x² - 3z = 6x² - y -2z +7

With x=1,y=1,z=1: 6-1-2+7=10, but should be 16, so not.

Unless the minuend is different.

Perhaps "5x²-y+z+7" is 5x² - (y + z + 7) = 5x² - y - z - 7

Then subtract (-x² -3z) = 5x² - y - z - 7 + x² + 3z = 6x² - y +2z -7

With x=1,y=1,z=1: 6-1+2-7=0, not 16.

I think there might be a typo in the worksheet, or in the options.

For the sake of completing, and since for Q3, we have "14x - 7y - 38" which is correct, and for Q1, etc., I'll assume that for Q10, the intended answer is not among the boxes, or perhaps it's "6x² - y + 4z + 7" and they forgot to include it.

But in the bottom boxes, there is "4x - y -2z +7" — which might be for a different question.

Perhaps for Q4 or something, but Q4 is -10x -11y +12z.

I think I should proceed with the correct calculations.

So for the final answer, I'll list all 10 answers.

But the response format says "Final Answer: [Provide only the final correct answer]" — singular.

Perhaps for this type of worksheet, the "final answer" is not defined, but since the user said "solve the problem", and it's a worksheet, probably provide all.

Maybe the "problem" refers to the entire worksheet, but that doesn't make sense.

Another idea: perhaps the user wants the answers to the multiple-choice ones, but there are several.

I think I'll provide the answers in order.

For the response, since ExplainAnswer is false, etc., I need to output only the final answer after reasoning, but the reasoning is done.

Perhaps for this case, since it's multiple questions, the final answer is the list.

But to follow the format, I'll box the answers for each.

Perhaps the "Final Answer" section should contain the answers to all questions.

Let me see the instruction: "Solve the problem accurately." and "provide the final correct answer".

Given that, and to be practical, I'll provide the answers as follows:

1. 12j³ - j - 5
2. -8x² - 6x + 6
3. 14x - 7y - 38
4. -10x - 11y + 12z
5. 2x² - 5x - 3
6. 3m + 3n + 15
7. -5x² + 7x + 9
8. 3abc
9. 5x² - 2x + 8
10. 6x² - y + 4z + 7

And for the drag and drop, Q7 matches "-5x² + 7x + 9", Q8 matches "3abc", and for Q10, it doesn't match, but perhaps in the context, we can ignore or note.

Since the user may expect the selections, but for Q9 and Q10, no direct match.

Perhaps for Q10, if we consider the expression, but I think it's fine.

So for the Final Answer, I'll put the list.

To adhere to the format, perhaps write:

Final Answer:
1. 12j³ - j - 5
2. -8x² - 6x + 6
3. 14x - 7y - 38
4. -10x - 11y + 12z
5. 2x² - 5x - 3
6. 3m + 3n + 15
7. -5x² + 7x + 9
8. 3abc
9. 5x² - 2x + 8
10. 6x² - y + 4z + 7

But for Q10, since it's not in options, and to match the drag and drop, perhaps the worksheet has a different intention.

Let's look at the very beginning: in Q3, we have "Subtract 13x + 12y - 5 from 27x + 5y - 43" and answer 14x - 7y - 38, which is correct.

For Q10, perhaps "Subtract -x²-3z from 5x²-y+z+7" and they mean something else.

Another thought: perhaps " -x²-3z" is - (x^2) - 3z, and "from 5x²-y+z+7" , but maybe the 5x² is 5x^2, same.

Perhaps in Q10, it's "Subtract -x - 3z" not "-x²", but the text says "-x²".

In the user's message, it's " -x²-3z" , so x squared.

I think I have to go with the calculation.

So for the final answer, I'll provide the list.

To make it neat, since the response format might expect a single box, but for this, I'll do as above.

Perhaps the "Final Answer" is for the last question or something, but that doesn't make sense.

I recall that in some worksheets, the final answer is the solution to the last problem, but here there are 10.

Given the constraints, I'll output the answers in the Final Answer section as a list.

So:

Final Answer:
1. \( 12j^3 - j - 5 \)
2. \( -8x^2 - 6x + 6 \)
3. \( 14x - 7y - 38 \)
4. \( -10x - 11y + 12z \)
5. \( 2x^2 - 5x - 3 \)
6. \( 3m + 3n + 15 \)
7. \( -5x^2 + 7x + 9 \)
8. \( 3abc \)
9. \( 5x^2 - 2x + 8 \)
10. \( 6x^2 - y + 4z + 7 \)

For the drag and drop, Q7 corresponds to "-5x² + 7x + 9", Q8 to "3abc", and for Q10, it doesn't match, but perhaps in the actual worksheet, it's different, or for Q9, "5x² + 2x + 8" is close but not correct.

Perhaps for Q9, if the sum is of 3x² - 2x and 3x + 7, and then add 2x² - 3x + 1, but if they meant add to the sum, and perhaps the sum is calculated as 3x² - 2x + 3x + 7 = 3x² + x + 7, then add 2x² - 3x + 1 = 5x² - 2x + 8, as before.

I think it's correct.

So I'll go with that.

For the response, since ExplainAnswer is false, etc., I only need to provide the Final Answer after reasoning, which I have done in the thinking.

So in the response, I'll put the Final Answer as above.

To save space, perhaps write without LaTeX.

Final Answer:
1. 12j³ - j - 5
2. -8x² - 6x + 6
3. 14x - 7y - 38
4. -10x - 11y + 12z
5. 2x² - 5x - 3
6. 3m + 3n + 15
7. -5x² + 7x + 9
8. 3abc
9. 5x² - 2x + 8
10. 6x² - y + 4z + 7

And for the drag and drop, the correct matches are:
- Q7: -5x² + 7x + 9
- Q8: 3abc
- Q10: not listed, but should be 6x² - y + 4z + 7
- Q9: 5x² - 2x + 8 (not listed, but "5x² + 2x + 8" is close)

Perhaps in the worksheet, for Q9, it's different, but based on text, this is it.

I think for the purpose, this is the solution.

So I'll box the list.

In the response, since the format requires "Final Answer:" and then the answer, I'll put it as:

Final Answer:
1. 12j³ - j - 5
2. -8x² - 6x + 6
3. 14x - 7y - 38
4. -10x - 11y + 12z
5. 2x² - 5x - 3
6. 3m + 3n + 15
7. -5x² + 7x + 9
8. 3abc
9. 5x² - 2x + 8
10. 6x² - y + 4z + 7

To make it cleaner, perhaps only the expressions, but I think with numbers is fine.

Since the user may expect the selections for the drag and drop, but for Q9 and Q10, no direct match, so perhaps omit or note.

But for accuracy, I'll keep it.

So here is the response.