Simplifying Variable Expressions worksheet with 22 algebra problems for practice.

Let’s solve each expression step by step. We’ll simplify them using basic algebra rules: distribute multiplication over addition, combine like terms, and remember that when multiplying variables with exponents, you add the exponents (like x² × x = x³).

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1) 5x²(5x + x) – x³

First, simplify inside the parentheses:
5x + x = 6x

Now multiply:
5x² × 6x = 30x³

Then subtract x³:
30x³ – x³ = 29x³

✔ Final Answer for #1: 29x³

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2) 21x + 7x²

These are not like terms — one has x, the other has x². Can’t combine.

Just write in standard form (highest power first):
7x² + 21x

✔ Final Answer for #2: 7x² + 21x

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3) 16x + 2x²

Again, different powers — can’t combine.

Write in standard form:
2x² + 16x

✔ Final Answer for #3: 2x² + 16x

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4) 3x²(5x + x) + x³

Simplify inside: 5x + x = 6x

Multiply: 3x² × 6x = 18x³

Add x³: 18x³ + x³ = 19x³

✔ Final Answer for #4: 19x³

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5) 11x²(5x + x) + x³

Inside: 5x + x = 6x

Multiply: 11x² × 6x = 66x³

Add x³: 66x³ + x³ = 67x³

✔ Final Answer for #5: 67x³

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6) 4x²(2x + x) – x³

Inside: 2x + x = 3x

Multiply: 4x² × 3x = 12x³

Subtract x³: 12x³ – x³ = 11x³

✔ Final Answer for #6: 11x³

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7) 8x²(2x)

Multiply coefficients: 8 × 2 = 16
Variables: x² × x = x³
→ 16x³

✔ Final Answer for #7: 16x³

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8) 5x + 4x²

Not like terms → reorder:
4x² + 5x

✔ Final Answer for #8: 4x² + 5x

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9) 16x²(6x + x)

Inside: 6x + x = 7x

Multiply: 16x² × 7x = 112x³

✔ Final Answer for #9: 112x³

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10) 6x + 4x²

Reorder:
4x² + 6x

✔ Final Answer for #10: 4x² + 6x

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11) 8x²(6x + x) – x³

Inside: 6x + x = 7x

Multiply: 8x² × 7x = 56x³

Subtract x³: 56x³ – x³ = 55x³

✔ Final Answer for #11: 55x³

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12) 12x + 6x²

Reorder:
6x² + 12x

✔ Final Answer for #12: 6x² + 12x

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13) 17x²(3x + x)

Inside: 3x + x = 4x

Multiply: 17x² × 4x = 68x³

✔ Final Answer for #13: 68x³

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14) 12x²(2x + x)

Inside: 2x + x = 3x

Multiply: 12x² × 3x = 36x³

✔ Final Answer for #14: 36x³

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15) 14x²(6x + x) – x³

Inside: 6x + x = 7x

Multiply: 14x² × 7x = 98x³

Subtract x³: 98x³ – x³ = 97x³

✔ Final Answer for #15: 97x³

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16) 10x + 7x²

Reorder:
7x² + 10x

✔ Final Answer for #16: 7x² + 10x

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17) 18x²(5x)

Multiply: 18 × 5 = 90; x² × x = x³ → 90x³

✔ Final Answer for #17: 90x³

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18) 2x²(4x)

2 × 4 = 8; x² × x = x³ → 8x³

✔ Final Answer for #18: 8x³

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19) 12x²(5x + x) + x³

Inside: 5x + x = 6x

Multiply: 12x² × 6x = 72x³

Add x³: 72x³ + x³ = 73x³

✔ Final Answer for #19: 73x³

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20) 15x²(4x + x)

Inside: 4x + x = 5x

Multiply: 15x² × 5x = 75x³

✔ Final Answer for #20: 75x³

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21) 15x²(2x + x) – x³

Inside: 2x + x = 3x

Multiply: 15x² × 3x = 45x³

Subtract x³: 45x³ – x³ = 44x³

✔ Final Answer for #21: 44x³

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22) 14x²(4x + x)

Inside: 4x + x = 5x

Multiply: 14x² × 5x = 70x³

✔ Final Answer for #22: 70x³

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Final Answer:
1) 29x³
2) 7x² + 21x
3) 2x² + 16x
4) 19x³
5) 67x³
6) 11x³
7) 16x³
8) 4x² + 5x
9) 112x³
10) 4x² + 6x
11) 55x³
12) 6x² + 12x
13) 68x³
14) 36x³
15) 97x³
16) 7x² + 10x
17) 90x³
18) 8x³
19) 73x³
20) 75x³
21) 44x³
22) 70x³