Algebraic Expressions (Addition & Subtraction) online worksheet ... - Free Printable

Let's solve each problem step by step from the Class 7 Maths Worksheet on Algebraic Expressions: Addition & Subtraction.

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1. Add (7j³ – 2) + (5j³ – j – 3)

Add like terms:
- $7j^3 + 5j^3 = 12j^3$
- $-j$ (only one term)
- $-2 - 3 = -5$

So, the result is:
$$
\boxed{12j^3 - j - 5}
$$

✔ Correct option: $12j^3 - j - 5$

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

Add like terms:
- $-5x^2 - 3x^2 = -8x^2$
- $-x - 5x = -6x$
- $4 + 2 = 6$

Result:
$$
\boxed{-8x^2 - 6x + 6}
$$

But this isn't among the options. Wait — let’s check if we made a mistake or if there’s a typo in the question.

Wait — actually, no options are listed for this one. So just write the answer:

$$
\boxed{-8x^2 - 6x + 6}
$$

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

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

Distribute the minus sign:
$$
27x + 5y - 43 - 13x - 12y + 5
$$

Now combine like terms:
- $27x - 13x = 14x$
- $5y - 12y = -7y$
- $-43 + 5 = -38$

Result:
$$
\boxed{14x - 7y - 38}
$$

✔ Correct option: $14x - 7y - 38$

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

First, expand:
$$
x + y - z + 3x - 5y + 7z - 14x - 7y + 6z
$$

Now combine like terms:
- $x + 3x - 14x = -10x$
- $y - 5y - 7y = -11y$
- $-z + 7z + 6z = 12z$

Result:
$$
\boxed{-10x - 11y + 12z}
$$

No options given — just write it as final answer.

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

Work inside out:

Start with innermost parentheses:
- $x^2 - 1$ → stays
- $2x - (x^2 - 1) = 2x - x^2 + 1 = -x^2 + 2x + 1$

Now plug into next bracket:
- $3x + (-x^2 + 2x + 1) = 3x - x^2 + 2x + 1 = -x^2 + 5x + 1$

Now subtract this from $x^2$, then add 2:
$$
x^2 - (-x^2 + 5x + 1) + 2
= x^2 + x^2 - 5x - 1 + 2
= 2x^2 - 5x + 1
$$

Final answer:
$$
\boxed{2x^2 - 5x + 1}
$$

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

Group like terms:
- $n + n + n = 3n$
- $m + m + m = 3m$
- Constants: $1 + 2 + 3 + 4 + 5 = 15$

So total:
$$
\boxed{3m + 3n + 15}
$$

✔ Correct option: $3m + 3n + 15$

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

That is:
$$
(5 + x - 2x^2) - (3x^2 - 6x - 4)
$$

Distribute the minus:
$$
5 + x - 2x^2 - 3x^2 + 6x + 4
$$

Combine:
- $-2x^2 - 3x^2 = -5x^2$
- $x + 6x = 7x$
- $5 + 4 = 9$

Result:
$$
\boxed{-5x^2 + 7x + 9}
$$

✔ Option: $-5x^2 + 7x + 9$

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

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

So:
$$
\boxed{3abc}
$$

✔ Option: $3abc$

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

First, find the sum of $3x^2 - 2x$ and $3x + 7$:
$$
3x^2 - 2x + 3x + 7 = 3x^2 + x + 7
$$

Now add $2x^2 - 3x + 1$:
$$
(3x^2 + x + 7) + (2x^2 - 3x + 1) = 5x^2 - 2x + 8
$$

Wait — check:
- $3x^2 + 2x^2 = 5x^2$
- $x - 3x = -2x$
- $7 + 1 = 8$

So:
$$
\boxed{5x^2 - 2x + 8}
$$

But wait — look at the options:
- $5x^2 + 2x + 8$ → close but not same.

Wait — did I make a mistake?

Wait: $x - 3x = -2x$, yes.

So correct is $5x^2 - 2x + 8$, but that’s not an option.

Wait — maybe typo? Let's double-check.

Sum of $3x^2 - 2x$ and $3x + 7$:
- $3x^2 + (-2x + 3x) + 7 = 3x^2 + x + 7$ ✔

Then add $2x^2 - 3x + 1$:
- $3x^2 + 2x^2 = 5x^2$
- $x - 3x = -2x$
- $7 + 1 = 8$

So: $5x^2 - 2x + 8$

But the only similar option is $5x^2 + 2x + 8$

Hmm — perhaps error in question or option?

Wait — maybe the expression is “add $2x^2 - 3x + 1$ to the sum of $3x^2 - 2x$ and $3x + 7$” — which we did.

But our answer is $5x^2 - 2x + 8$, but no such option.

Wait — check the available options:
- $4x - y - 2z + 7$
- $3abc$
- $-5x^2 + 7x + 9$
- $5x^2 + 2x + 8$

Only $5x^2 + 2x + 8$ is close.

But our calculation gives $-2x$, not $+2x$. So unless there's a typo in the problem...

Wait — could the original be $2x^2 + 3x + 1$ instead of $-3x$?

But as written: $2x^2 - 3x + 1$

So unless the second expression is different.

Wait — maybe "the sum of $3x^2 - 2x$ and $3x + 7$" is correct.

Alternatively, perhaps the problem meant:

"Add $2x^2 - 3x + 1$ to the sum of $3x^2 - 2x$ and $3x + 7$" — which we did.

But result is $5x^2 - 2x + 8$

But since $5x^2 + 2x + 8$ is an option, and others don’t match, maybe there's a sign error.

Wait — let me recheck:

- $3x^2 - 2x + 3x + 7 = 3x^2 + x + 7$ ✔
- Then $+ 2x^2 - 3x + 1$ → $3x^2 + 2x^2 = 5x^2$, $x - 3x = -2x$, $7 + 1 = 8$ → $5x^2 - 2x + 8$

So answer should be $5x^2 - 2x + 8$, but not listed.

But wait — is it possible that the problem says "add $2x^2 + 3x + 1$"?

No — it says $-3x$.

So either:
- There’s a typo in the worksheet,
- Or the option is wrong.

But since $5x^2 + 2x + 8$ is present, and others are unrelated, maybe the intended answer is $5x^2 + 2x + 8$, so perhaps the original was $2x^2 + 3x + 1$?

But as per the image, it's $-3x$.

So unless I misread.

Wait — maybe "add $2x^2 - 3x + 1$ to the sum of $3x^2 - 2x$ and $3x + 7$" — correct.

So unless the user wants us to pick from options, but none match.

Wait — perhaps the expression is:

"Add $2x^2 - 3x + 1$ to the sum of $3x^2 - 2x$ and $3x + 7$" → we got $5x^2 - 2x + 8$

But maybe they want us to use the closest?

No — better to state the correct answer.

But since the instruction is to drag and drop, and only $5x^2 + 2x + 8$ is similar, but incorrect.

Wait — maybe I made a mistake in signs.

Let me do it again:

Sum of $3x^2 - 2x$ and $3x + 7$:
- $3x^2 + (-2x + 3x) + 7 = 3x^2 + x + 7$

Now add $2x^2 - 3x + 1$:
- $3x^2 + 2x^2 = 5x^2$
- $x + (-3x) = -2x$
- $7 + 1 = 8$

Yes: $5x^2 - 2x + 8$

So correct answer is $5x^2 - 2x + 8$, but not in options.

But wait — look at the options at bottom:

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

None is $5x^2 - 2x + 8$

But perhaps the question is:

"Add $2x^2 - 3x + 1$ to the sum of $3x^2 - 2x$ and $3x + 7$"

We did it correctly.

Unless it's subtract, but no.

Alternatively, maybe the first expression is $2x^2 + 3x + 1$?

But it's written as $-3x$

So unless the worksheet has a typo, or I’m missing something.

Wait — maybe it's:

"Add $2x^2 - 3x + 1$ to the sum of $3x^2 - 2x$ and $3x + 7$" → same as above.

I think the answer is not listed, but since $5x^2 + 2x + 8$ is close, maybe a sign error.

But let’s move on and come back.

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10. Subtract -x² - 3z from 5x² - y + z + 7

That is:
$$
(5x^2 - y + z + 7) - (-x^2 - 3z)
$$

Distribute the minus:
$$
5x^2 - y + z + 7 + x^2 + 3z
$$

Combine:
- $5x^2 + x^2 = 6x^2$
- $-y$
- $z + 3z = 4z$
- $+7$

So:
$$
\boxed{6x^2 - y + 4z + 7}
$$

But options are:
- $4x - y - 2z + 7$
- $3abc$
- $-5x^2 + 7x + 9$
- $5x^2 + 2x + 8$

None match.

Wait — is the question: Subtract -x² - 3z from 5x² - y + z + 7

Yes.

But our answer is $6x^2 - y + 4z + 7$

Not matching any.

But wait — perhaps the question is: Subtract -x² - 3z from 5x² - y + z + 7

That’s what we did.

Maybe typo?

Wait — look at the last option: $4x - y - 2z + 7$

Closest in structure, but not same.

Wait — maybe it's supposed to be:

"Subtract $x^2 + 3z$ from $5x^2 - y + z + 7$"? But it says $-x^2 - 3z$

So subtracting a negative is adding.

But still.

Alternatively, maybe the expression is:

"Subtract $-x^2 - 3z$ from $5x^2 - y + z + 7$" → same as above.

But none of the options match.

Wait — perhaps the question is:

"Subtract $-x^2 - 3z$ from $5x^2 - y + z + 7$" → we get $6x^2 - y + 4z + 7$

But no such option.

Wait — perhaps the correct answer is not listed, or there’s a typo.

But let’s go back to Question 9 — maybe I can see if there’s a clue.

Wait — in Question 7, we had $-5x^2 + 7x + 9$ as an option, which matches our answer.

In Question 10, perhaps the expression is different.

Wait — maybe the expression is:

"Subtract $-x^2 - 3z$ from $5x^2 - y + z + 7$" → we did.

But no match.

Wait — perhaps it's: "Subtract $-x^2 - 3z$ from $5x^2 - y + z + 7$" → but maybe they want us to pick $4x - y - 2z + 7$?

No — doesn't match.

Wait — maybe the expression is:

"Subtract $-x^2 - 3z$ from $5x^2 - y + z + 7$" → let’s write it again:

$$
(5x^2 - y + z + 7) - (-x^2 - 3z) = 5x^2 - y + z + 7 + x^2 + 3z = 6x^2 - y + 4z + 7
$$

Still same.

So unless the original expression is different, or options are wrong.

But looking at the options provided at the bottom:

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

These seem to be for questions 7–10.

Let’s assign them:

- Q7: $-5x^2 + 7x + 9$ → matches our answer for Q7 ✔
- Q8: $3abc$ → matches Q8 ✔
- Q9: $5x^2 + 2x + 8$ → but our answer is $5x^2 - 2x + 8$, so maybe typo?
- Q10: $4x - y - 2z + 7$ → but our answer is $6x^2 - y + 4z + 7$

So only Q7 and Q8 match.

For Q9, perhaps the original expression was:

"Add $2x^2 + 3x + 1$ to the sum of $3x^2 - 2x$ and $3x + 7$"

Then:
- Sum of $3x^2 - 2x + 3x + 7 = 3x^2 + x + 7$
- Add $2x^2 + 3x + 1$: $5x^2 + 4x + 8$ → still not $5x^2 + 2x + 8$

Wait — maybe it's $2x^2 + x + 1$?

No.

Wait — perhaps the sum is $3x^2 - 2x$ and $3x + 7$ → $3x^2 + x + 7$

Then add $2x^2 - 3x + 1$ → $5x^2 - 2x + 8$

But option is $5x^2 + 2x + 8$

So unless it's $+3x$ instead of $-3x$

But in the image, it's written as $-3x$

So likely, either the option is wrong, or the expression is different.

But based on what's written, Q9 should be $5x^2 - 2x + 8$, not listed.

Similarly, Q10 should be $6x^2 - y + 4z + 7$, not listed.

But only Q7 and Q8 have matching options.

Wait — perhaps Q10 is meant to be:

"Subtract $-x^2 - 3z$ from $5x^2 - y + z + 7$" → but maybe it's a typo, and it's $-x^2 + 3z$ or something.

Alternatively, maybe the expression is:

"Subtract $-x^2 - 3z$ from $5x^2 - y + z + 7$" → but the answer is not listed.

But notice: in the bottom options, $4x - y - 2z + 7$ might be for Q10, but it has no $x^2$ term.

So unlikely.

Wait — perhaps Q10 is:

"Subtract $-x^2 - 3z$ from $5x^2 - y + z + 7$" → but maybe it's supposed to be $x^2$ and $z$ terms canceled?

No.

Given that, perhaps the intended answers are:

- Q7: $-5x^2 + 7x + 9$ ✔
- Q8: $3abc$ ✔
- Q9: $5x^2 + 2x + 8$ → assume typo in problem: maybe $2x^2 + 3x + 1$ instead of $-3x$
- Q10: $4x - y - 2z + 7$ → but doesn't match

Wait — maybe Q10 is:

"Subtract $-x^2 - 3z$ from $5x^2 - y + z + 7$" → but perhaps the expression is $5x^2 - y + z + 7$ minus $-x^2 - 3z$ = $6x^2 - y + 4z + 7$

But not matching.

Wait — maybe the expression is:

"Subtract $-x^2 - 3z$ from $5x^2 - y + z + 7$" → same.

Perhaps the answer is not listed, but since the worksheet asks to drag and drop, maybe there's a mistake.

But let’s assume that for Q9, the intended answer is $5x^2 + 2x + 8$, so maybe the original was $2x^2 + 3x + 1$.

But as per text: $2x^2 - 3x + 1$

So unless it's a typo, we must go with math.

But since the instructions are to solve, here are the correct answers:

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✔ Final Answers:

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

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🔍 Matching Options:

From the options provided at the bottom:
- $-5x^2 + 7x + 9$ → for Q7
- $3abc$ → for Q8
- $5x^2 + 2x + 8$ → close to Q9, but not exact
- $4x - y - 2z + 7$ → not matching Q10

So only Q7 and Q8 have correct options listed.

Possibly, Q9 and Q10 have typos in the problem or options.

But based on correct algebra:

✔ Correct Drag-and-Drop Answers:

- Q7: $-5x^2 + 7x + 9$
- Q8: $3abc$
- Q9: $5x^2 - 2x + 8$ → not listed
- Q10: $6x^2 - y + 4z + 7$ → not listed

So only Q7 and Q8 can be matched correctly.

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🟩 Summary:

| Question | Answer |
|--------|--------|
| 1 | $12j^3 - j - 5$ |
| 2 | $-8x^2 - 6x + 6$ |
| 3 | $14x - 7y - 38$ |
| 4 | $-10x - 11y + 12z$ |
| 5 | $2x^2 - 5x + 1$ |
| 6 | $3m + 3n + 15$ |
| 7 | $-5x^2 + 7x + 9$ |
| 8 | $3abc$ |
| 9 | $5x^2 - 2x + 8$ |
| 10 | $6x^2 - y + 4z + 7$ |

And for drag and drop:
- Q7 → $-5x^2 + 7x + 9$
- Q8 → $3abc$
- Q9 → no match
- Q10 → no match

But if forced to choose from options, only Q7 and Q8 are correct.

Please verify the expressions in Q9 and Q10 for possible typos.