Simplifying Polynomial Expressions Worksheets - Free Printable

Let's go through each polynomial expression step by step and simplify them. We'll combine like terms, distribute where necessary, and simplify as much as possible.

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1) $ 4x^2 + 2 - 5x^2 + 6x^8 - 13 - x^8 $

Step 1: Group like terms:
- $ 6x^8 - x^8 = 5x^8 $
- $ 4x^2 - 5x^2 = -x^2 $
- $ 2 - 13 = -11 $

Simplified:
$$
5x^8 - x^2 - 11
$$

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2) $ 2y^3 + 3y - 5y^3 + y^5 $

Step 1: Group like terms:
- $ 2y^3 - 5y^3 = -3y^3 $
- $ y^5 $ (only one term)
- $ 3y $ (only one term)

Simplified:
$$
y^5 - 3y^3 + 3y
$$

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3) $ -(9t^2 - 2) + 15 - 8t^2 - 2 $

Step 1: Distribute the negative sign:
$$
-9t^2 + 2 + 15 - 8t^2 - 2
$$

Step 2: Combine like terms:
- $ -9t^2 - 8t^2 = -17t^2 $
- $ 2 + 15 - 2 = 15 $

Simplified:
$$
-17t^2 + 15
$$

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4) $ u^4 - u^2(3u^2 - 2) $

Step 1: Distribute $ u^2 $ into the parentheses:
$$
u^4 - [u^2 \cdot 3u^2 - u^2 \cdot 2] = u^4 - (3u^4 - 2u^2)
$$

Step 2: Distribute the negative sign:
$$
u^4 - 3u^4 + 2u^2 = -2u^4 + 2u^2
$$

Simplified:
$$
-2u^4 + 2u^2
$$

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5) $ 14 - 5(2p^2 - 12p^3) - 3p^3 - 8 $

Step 1: Distribute the $-5$:
$$
14 - 5 \cdot 2p^2 + 5 \cdot 12p^3 - 3p^3 - 8 = 14 - 10p^2 + 60p^3 - 3p^3 - 8
$$

Step 2: Combine like terms:
- $ 60p^3 - 3p^3 = 57p^3 $
- $ -10p^2 $ (only one)
- $ 14 - 8 = 6 $

Simplified:
$$
57p^3 - 10p^2 + 6
$$

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6) $ 7a^2 + 13 - 8a^2 $

Step 1: Combine like terms:
- $ 7a^2 - 8a^2 = -a^2 $
- $ 13 $ remains

Simplified:
$$
-a^2 + 13
$$

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7) $ -18 + 9b^2 + 6 $

Step 1: Combine constants:
- $ -18 + 6 = -12 $

Simplified:
$$
9b^2 - 12
$$

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8) $ -11 - 9(2y^2 + 7y^3) + 8y^2 + 1 $

Step 1: Distribute the $-9$:
$$
-11 - 9 \cdot 2y^2 - 9 \cdot 7y^3 + 8y^2 + 1 = -11 - 18y^2 - 63y^3 + 8y^2 + 1
$$

Step 2: Combine like terms:
- $ -63y^3 $ (only one)
- $ -18y^2 + 8y^2 = -10y^2 $
- $ -11 + 1 = -10 $

Simplified:
$$
-63y^3 - 10y^2 - 10
$$

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✔ Final Answers:

1) $ 5x^8 - x^2 - 11 $
2) $ y^5 - 3y^3 + 3y $
3) $ -17t^2 + 15 $
4) $ -2u^4 + 2u^2 $
5) $ 57p^3 - 10p^2 + 6 $
6) $ -a^2 + 13 $
7) $ 9b^2 - 12 $
8) $ -63y^3 - 10y^2 - 10 $

Let me know if you'd like these written in a specific format or need help with any particular step!