Algebraic Expressions | Worksheet - Free Printable

Let’s solve each problem step by step. We’ll go section by section.

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Section 1: Simplify the following expressions

These are all about combining like terms — that means adding or subtracting numbers with the same variable (like “a” or “b”).

1) 5a + 6a
→ Both have “a”, so add 5 + 6 = 11 → 11a

2) 3a + a
→ “a” is the same as “1a”, so 3a + 1a = 4a → 4a

3) 3a - 3a
→ Same thing, subtract: 3 - 3 = 0 → 0

4) 10a - 2a
→ 10 - 2 = 8 → 8a

5) 9a + 4a
→ 9 + 4 = 13 → 13a

6) 11a - 7a
→ 11 - 7 = 4 → 4a

7) 4b + 3b
→ 4 + 3 = 7 → 7b

8) 12b - 6b
→ 12 - 6 = 6 → 6b

9) 5b + 9b
→ 5 + 9 = 14 → 14b

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Section 2: Complete the following expressions

These are just arithmetic problems — no variables. Do them left to right unless there are parentheses (but here, none).

1) 12 + 3 - 5 + 4
→ 12 + 3 = 15
→ 15 - 5 = 10
→ 10 + 4 = 14

2) 4 + 7 + 2 - 8
→ 4 + 7 = 11
→ 11 + 2 = 13
→ 13 - 8 = 5

3) 5 - 7 + 2 + 10
→ 5 - 7 = -2
→ -2 + 2 = 0
→ 0 + 10 = 10

4) 15 + 3 - 8 + 5
→ 15 + 3 = 18
→ 18 - 8 = 10
→ 10 + 5 = 15

5) 11 + 3 - 12 + 4
→ 11 + 3 = 14
→ 14 - 12 = 2
→ 2 + 4 = 6

6) 5 + 9 - 16 + 2
→ 5 + 9 = 14
→ 14 - 16 = -2
→ -2 + 2 = 0

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Section 3: Combine like terms to simplify the following expressions

Now we mix numbers and variables. Group the “a” terms together and the number terms together.

1) 3a(a + 4) - 2a + 7
Wait — this has multiplication! Let’s expand first:

→ 3a × a = 3a²
→ 3a × 4 = 12a
So now: 3a² + 12a - 2a + 7
Combine like terms: 12a - 2a = 10a
Final: 3a² + 10a + 7

But wait — looking back at the original worksheet, it says “Combine like terms to simplify...” and the expression is written as:

> 1.) 3a(a + 4) - 2a + 7

This might be a typo? Because if it’s meant to be linear (no squares), maybe it was supposed to be 3(a + 4) - 2a + 7? But let’s stick to what’s written.

Actually, rechecking — in many middle school worksheets, sometimes they write “3a(a+4)” meaning 3 times a times (a+4), which gives a squared term. But let’s see other problems — problem 4 has “2(1 - 7)(4 + a)”, which also suggests multiplication.

Hold on — perhaps these are not algebraic simplifications with distribution, but rather miswritten? Let me check the pattern.

Looking again at Section 3:

Problem 1: 3a(a + 4) - 2a + 7 → This would give 3a² + 12a - 2a + 7 = 3a² + 10a + 7

But Problem 2: 5a + 3a - 15 + 3 → That’s straightforward: 8a - 12

Problem 3: 4(3 + 9) + 10a - 4a → First, 4×12 = 48, then 10a - 4a = 6a → 48 + 6a

Problem 4: 2(1 - 7)(4 + a) - 12 → First, (1-7)= -6, then 2×(-6)= -12, then -12×(4+a) = -48 -12a, then -48 -12a -12 = -60 -12a

Problem 5: 17 + 4(5 + a) - a → 4×5=20, 4×a=4a → 17 + 20 + 4a - a = 37 + 3a

Problem 6: 10a - 4a + 27 - 3 → 6a + 24

So yes, some involve distribution. Let’s do them carefully.

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Section 3 Redone Carefully:

1) 3a(a + 4) - 2a + 7
→ Distribute 3a: 3a * a = 3a², 3a * 4 = 12a
→ So: 3a² + 12a - 2a + 7
→ Combine: 12a - 2a = 10a
→ Final: 3a² + 10a + 7

2) 5a + 3a - 15 + 3
→ 5a + 3a = 8a
→ -15 + 3 = -12
→ Final: 8a - 12

3) 4(3 + 9) + 10a - 4a
→ Inside parentheses: 3 + 9 = 12
→ 4 × 12 = 48
→ 10a - 4a = 6a
→ Final: 48 + 6a or 6a + 48

4) 2(1 - 7)(4 + a) - 12
→ First: 1 - 7 = -6
→ Then: 2 × (-6) = -12
→ Now: -12 × (4 + a) = -48 -12a
→ Then: -48 -12a - 12 = -60 -12a
→ Final: -12a - 60

5) 17 + 4(5 + a) - a
→ Distribute 4: 4×5=20, 4×a=4a
→ So: 17 + 20 + 4a - a
→ Numbers: 17 + 20 = 37
→ Variables: 4a - a = 3a
→ Final: 3a + 37

6) 10a - 4a + 27 - 3
→ 10a - 4a = 6a
→ 27 - 3 = 24
→ Final: 6a + 24

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Now, let’s compile all answers clearly.

Final Answer:

Section 1: Simplify
1) 11a
2) 4a
3) 0
4) 8a
5) 13a
6) 4a
7) 7b
8) 6b
9) 14b

Section 2: Complete
1) 14
2) 5
3) 10
4) 15
5) 6
6) 0

Section 3: Combine like terms
1) 3a² + 10a + 7
2) 8a - 12
3) 6a + 48
4) -12a - 60
5) 3a + 37
6) 6a + 24