### About Multiplying Polynomials:

When we multiply two polynomials together, we use our associative, commutative, and distributive properties, along with our rules for exponents. To multiply two binomials together quickly, we use a shortcut known as FOIL. Lastly, when we multiply more than two polynomials, we find the product of any two first, and continue multiplying until we have our product.

Test Objectives

- Demonstrate the ability to find the product of two polynomials
- Demonstrate the ability to find the product of two binomials using FOIL
- Demonstrate the ability to find the product of more than two polynomials

#1:

Instructions: Find each product.

a) 4n(6n^{2} + 8n - 3)

b) (2x - 5y)(3x + 3y)

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#2:

Instructions: Find each product.

a) (6n - 4)(5n + 6)

b) (x - 4y)(2x - 3y)

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#3:

Instructions: Find each product.

a) (10x - 7)(2x^{2} - 2x - 3)

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#4:

Instructions: Find each product.

a) (14x^{2} - 14x - 4)(10x^{2} - 6x - 9)

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#5:

Instructions: Find each product.

a) (4a - b)(5a + 3b)(a^{2} - 2b + 7ab)

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Written Solutions:

#1:

Solutions:

a) 24n^{3} + 32n^{2} - 12n

b) 6x^{2} - 9xy - 15y^{2}

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#2:

Solutions:

a) 30n^{2} + 16n - 24

b) 2x^{2} - 11xy + 12y^{2}

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#3:

Solutions:

a) 20x^{3} - 34x^{2} - 16x + 21

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#4:

Solutions:

a) 140x^{4} - 224x^{3} - 82x^{2} + 150x + 36

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#5:

Solutions:

a) 20a^{4} - 40a^{2}b + 147a^{3}b - 14ab^{2} + 46a^{2}b^{2} + 6b^{3} - 21ab^{3}