### About Multiplying Polynomials:

We continue to focus on the topic of polynomials. Here we will learn how to multiply two or more polynomials together. To multiply two polynomials together, we multiply each term of the first polynomial by each term of the second polynomial. Lastly, we combine like terms.

Test Objectives

- Demonstrate an understanding of the rules of exponents
- Demonstrate the ability to multiply two or more polynomials
- Demonstrate the ability to combine like terms

#1:

Instructions: Find each product.

a) -4a(-7a + 6)

b) -2(-4n - 6)

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#2:

Instructions: Find each product.

a) 8b^{3}(8b - 4)

b) (4n - 4)(-7n - 6)

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#3:

Instructions: Find each product.

a) (-5n + 5)(-8n + 4)

b)$$\left(\frac{5r}{2} - \frac{5}{2}\right)\left(\frac{5r}{2}-\frac{10}{3}\right)$$

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#4:

Instructions: Find each product.

a) (8p^{2} + 3p - 1)(p^{2} + 5p + 5)

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#5:

Instructions: Find each product.

a) (2x^{2} - x + 3)(2x^{2} + 2x + 1)(-5x - 1)

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Written Solutions:

#1:

Solutions:

a) 28a^{2} - 24a

b) 8n + 12

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#2:

Solutions:

a) 64b^{4} - 32b^{3}

b) -28n^{2} + 4n + 24

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#3:

Solutions:

a) 40n^{2} - 60n + 20

b)

25r^{2} |
- | 175r | + | 25 |

4 | 12 | 3 |

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#4:

Solutions:

a) 8p^{4} + 43p^{3} + 54p^{2} + 10p - 5

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#5:

Solutions:

a) -20x^{5} - 14x^{4} - 32x^{3} - 31x^{2} - 20x - 3