Simplifying Expressions Worksheets - Math Monks - Free Printable

Let's go through each expression one by one and simplify them step by step.

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1. $ 2x^2 - 10x^2 + 9x $

Combine like terms:
- $ 2x^2 - 10x^2 = -8x^2 $
- $ 9x $ remains as is (no other $ x $ terms)

✔ Answer: $ -8x^2 + 9x $

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2. $ 7a^2 + 8a + 9a^2 $

Combine like terms:
- $ 7a^2 + 9a^2 = 16a^2 $
- $ 8a $ remains

✔ Answer: $ 16a^2 + 8a $

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3. $ 5 \cdot 5x^2 \cdot (-5x) $

Multiply the coefficients and variables:
- Coefficients: $ 5 \cdot 5 \cdot (-5) = -125 $
- Variables: $ x^2 \cdot x = x^3 $

So: $ -125x^3 $

✔ Answer: $ -125x^3 $

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4. $ -1 - a^2 - 4a^2 $

Combine like terms:
- $ -a^2 - 4a^2 = -5a^2 $
- $ -1 $ remains

✔ Answer: $ -5a^2 - 1 $

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5. $ -x^2 - 1 - 5x^2 $

Combine like terms:
- $ -x^2 - 5x^2 = -6x^2 $
- $ -1 $ remains

✔ Answer: $ -6x^2 - 1 $

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6. $ -1 + 1 - c^2 $

Simplify constants:
- $ -1 + 1 = 0 $
- So we're left with $ -c^2 $

✔ Answer: $ -c^2 $

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7. $ 2 + 8z^2 + 1 $

Combine constants:
- $ 2 + 1 = 3 $
- $ 8z^2 $ remains

✔ Answer: $ 8z^2 + 3 $

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8. $ x^2 - x - x $

Combine like terms:
- $ -x - x = -2x $
- $ x^2 $ remains

✔ Answer: $ x^2 - 2x $

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9. $ -\frac{u^2}{-u^2} \cdot (-u^2) $

First, simplify $ -\frac{u^2}{-u^2} $:

- $ \frac{u^2}{-u^2} = -1 $, so $ -(-1) = 1 $

Now multiply by $ (-u^2) $:
- $ 1 \cdot (-u^2) = -u^2 $

✔ Answer: $ -u^2 $

> Alternatively, step-by-step:
> $$
> -\frac{u^2}{-u^2} \cdot (-u^2) = -(-1) \cdot (-u^2) = 1 \cdot (-u^2) = -u^2
> $$

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10. $ -a \cdot \frac{7a^2}{a} $

First simplify $ \frac{7a^2}{a} $:
- $ \frac{a^2}{a} = a $, so $ \frac{7a^2}{a} = 7a $

Now multiply by $ -a $:
- $ -a \cdot 7a = -7a^2 $

✔ Answer: $ -7a^2 $

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✔ Final Answers:

1. $ -8x^2 + 9x $
2. $ 16a^2 + 8a $
3. $ -125x^3 $
4. $ -5a^2 - 1 $
5. $ -6x^2 - 1 $
6. $ -c^2 $
7. $ 8z^2 + 3 $
8. $ x^2 - 2x $
9. $ -u^2 $
10. $ -7a^2 $

Let me know if you'd like these explained in more detail!