Math worksheet for simplifying algebraic expressions by combining like terms with exponents.

Sure! Let’s solve each problem step by step, combining like terms. “Like terms” are terms that have the same variable(s) raised to the same power(s). We can only combine those.

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Part 1: Simplify each sum by combining like terms

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① (2a³ - 7a²) + (3a² + 3a³)

Step 1: Remove parentheses (since it’s addition, signs stay the same):

> 2a³ - 7a² + 3a² + 3a³

Step 2: Group like terms:

> (2a³ + 3a³) + (-7a² + 3a²)

Step 3: Combine coefficients:

> 5a³ - 4a²

✔ Answer: 5a³ - 4a²

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② (1 - 5a⁴) + (8a⁴ + 3)

Step 1: Remove parentheses:

> 1 - 5a⁴ + 8a⁴ + 3

Step 2: Group like terms:

> (-5a⁴ + 8a⁴) + (1 + 3)

Step 3: Combine:

> 3a⁴ + 4

✔ Answer: 3a⁴ + 4

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③ (-13k⁵ - 6 - 9k) + (3k⁵ + 8 + 8k)

Step 1: Remove parentheses:

> -13k⁵ - 6 - 9k + 3k⁵ + 8 + 8k

Step 2: Group like terms:

> (-13k⁵ + 3k⁵) + (-9k + 8k) + (-6 + 8)

Step 3: Combine:

> -10k⁵ - k + 2

✔ Answer: -10k⁵ - k + 2

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④ 6(4x² - 5x + 2) + 3(-8x² + 11x + 4)

Step 1: Distribute the numbers outside the parentheses:

> 6·4x² = 24x²
> 6·(-5x) = -30x
> 6·2 = 12
>
> 3·(-8x²) = -24x²
> 3·11x = 33x
> 3·4 = 12

So we get:

> 24x² - 30x + 12 - 24x² + 33x + 12

Step 2: Group like terms:

> (24x² - 24x²) + (-30x + 33x) + (12 + 12)

Step 3: Combine:

> 0x² + 3x + 24 → 3x + 24

✔ Answer: 3x + 24

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Part 2: Simplify each difference by combining like terms

*(Remember: subtracting a group means distributing the minus sign to every term inside!)*

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⑤ 4(6x³ - 4x² + 7x + 1) - 9(4x³ - 2x² - 6x + 1)

Step 1: Distribute both numbers:

> 4·6x³ = 24x³
> 4·(-4x²) = -16x²
> 4·7x = 28x
> 4·1 = 4
>
> -9·4x³ = -36x³
> -9·(-2x²) = +18x²
> -9·(-6x) = +54x
> -9·1 = -9

Now write all together:

> 24x³ - 16x² + 28x + 4 - 36x³ + 18x² + 54x - 9

Step 2: Group like terms:

> (24x³ - 36x³) + (-16x² + 18x²) + (28x + 54x) + (4 - 9)

Step 3: Combine:

> -12x³ + 2x² + 82x - 5

✔ Answer: -12x³ + 2x² + 82x - 5

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⑥ 10(4x² + 8x + 7) - 8(5x² + 10x - 9)

Step 1: Distribute:

> 10·4x² = 40x²
> 10·8x = 80x
> 10·7 = 70
>
> -8·5x² = -40x²
> -8·10x = -80x
> -8·(-9) = +72

So:

> 40x² + 80x + 70 - 40x² - 80x + 72

Step 2: Group like terms:

> (40x² - 40x²) + (80x - 80x) + (70 + 72)

Step 3: Combine:

> 0x² + 0x + 142 → 142

✔ Answer: 142

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⑦ 3(16x⁴ - 16x³ + 2x² - 8x + 24) - 4(8x⁴ - 12x³ - 2x² - 4x + 16)

Step 1: Distribute:

First part:
> 3·16x⁴ = 48x⁴
> 3·(-16x³) = -48x³
> 3·2x² = 6x²
> 3·(-8x) = -24x
> 3·24 = 72

Second part (remember to distribute the negative!):
> -4·8x⁴ = -32x⁴
> -4·(-12x³) = +48x³
> -4·(-2x²) = +8x²
> -4·(-4x) = +16x
> -4·16 = -64

Now put all together:

> 48x⁴ - 48x³ + 6x² - 24x + 72 - 32x⁴ + 48x³ + 8x² + 16x - 64

Step 2: Group like terms:

> (48x⁴ - 32x⁴) + (-48x³ + 48x³) + (6x² + 8x²) + (-24x + 16x) + (72 - 64)

Step 3: Combine:

> 16x⁴ + 0x³ + 14x² - 8x + 8

✔ Answer: 16x⁴ + 14x² - 8x + 8

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## ✔ Final Answers:

① 5a³ - 4a²
② 3a⁴ + 4
③ -10k⁵ - k + 2
④ 3x + 24
⑤ -12x³ + 2x² + 82x - 5
⑥ 142
⑦ 16x⁴ + 14x² - 8x + 8

Let me know if you’d like to see any step explained in more detail!