Multiplying Polynomials Practice Worksheet A featuring eight problems to find products by multiplying polynomials.

Let's solve each of the polynomial multiplication problems step by step using the distributive property (also known as the FOIL method for binomials). We will expand each expression and combine like terms.

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1) (x + 4)(x + 5)

Use FOIL:
- First: $ x \cdot x = x^2 $
- Outer: $ x \cdot 5 = 5x $
- Inner: $ 4 \cdot x = 4x $
- Last: $ 4 \cdot 5 = 20 $

Add them:
$ x^2 + 5x + 4x + 20 = x^2 + 9x + 20 $

✔ Answer: $ x^2 + 9x + 20 $

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2) (x + 9)(x - 2)

FOIL:
- First: $ x \cdot x = x^2 $
- Outer: $ x \cdot (-2) = -2x $
- Inner: $ 9 \cdot x = 9x $
- Last: $ 9 \cdot (-2) = -18 $

Add:
$ x^2 - 2x + 9x - 18 = x^2 + 7x - 18 $

✔ Answer: $ x^2 + 7x - 18 $

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3) (2x - 8)(x + 6)

Distribute each term:
- $ 2x(x + 6) = 2x^2 + 12x $
- $ -8(x + 6) = -8x - 48 $

Add:
$ 2x^2 + 12x - 8x - 48 = 2x^2 + 4x - 48 $

✔ Answer: $ 2x^2 + 4x - 48 $

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4) (2x + 3)(4x - 5)

FOIL:
- First: $ 2x \cdot 4x = 8x^2 $
- Outer: $ 2x \cdot (-5) = -10x $
- Inner: $ 3 \cdot 4x = 12x $
- Last: $ 3 \cdot (-5) = -15 $

Add:
$ 8x^2 - 10x + 12x - 15 = 8x^2 + 2x - 15 $

✔ Answer: $ 8x^2 + 2x - 15 $

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5) (5x - 6)(3x + 9)

FOIL:
- First: $ 5x \cdot 3x = 15x^2 $
- Outer: $ 5x \cdot 9 = 45x $
- Inner: $ -6 \cdot 3x = -18x $
- Last: $ -6 \cdot 9 = -54 $

Add:
$ 15x^2 + 45x - 18x - 54 = 15x^2 + 27x - 54 $

✔ Answer: $ 15x^2 + 27x - 54 $

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6) (8x - 1)(2x - 3)

FOIL:
- First: $ 8x \cdot 2x = 16x^2 $
- Outer: $ 8x \cdot (-3) = -24x $
- Inner: $ -1 \cdot 2x = -2x $
- Last: $ -1 \cdot (-3) = 3 $

Add:
$ 16x^2 - 24x - 2x + 3 = 16x^2 - 26x + 3 $

✔ Answer: $ 16x^2 - 26x + 3 $

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7) (3x + 2)(x² - 2x + 1)

Use distributive property (multiply each term in the first polynomial by each in the second):

- $ 3x(x^2) = 3x^3 $
- $ 3x(-2x) = -6x^2 $
- $ 3x(1) = 3x $
- $ 2(x^2) = 2x^2 $
- $ 2(-2x) = -4x $
- $ 2(1) = 2 $

Now add all:
$ 3x^3 - 6x^2 + 3x + 2x^2 - 4x + 2 $

Combine like terms:
- $ 3x^3 $
- $ (-6x^2 + 2x^2) = -4x^2 $
- $ (3x - 4x) = -x $
- $ +2 $

✔ Answer: $ 3x^3 - 4x^2 - x + 2 $

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8) (2x² - x)(3x - 1)

Distribute each term:

- $ 2x^2(3x) = 6x^3 $
- $ 2x^2(-1) = -2x^2 $
- $ -x(3x) = -3x^2 $
- $ -x(-1) = x $

Add:
$ 6x^3 - 2x^2 - 3x^2 + x = 6x^3 - 5x^2 + x $

✔ Answer: $ 6x^3 - 5x^2 + x $

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✔ Final Answers:

1) $ x^2 + 9x + 20 $
2) $ x^2 + 7x - 18 $
3) $ 2x^2 + 4x - 48 $
4) $ 8x^2 + 2x - 15 $
5) $ 15x^2 + 27x - 54 $
6) $ 16x^2 - 26x + 3 $
7) $ 3x^3 - 4x^2 - x + 2 $
8) $ 6x^3 - 5x^2 + x $

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