### About FOIL:

When multiplying polynomials, we will often come across the product of two binomials. A common method to solve this problem is known as FOIL. This tells us the order to multiply: first terms, outer terms, inner terms, and last terms. We finish by combining like terms.

Test Objectives

- Demonstrate the ability to multiply two binomials using FOIL
- Demonstrate the ability to utilize FOIL when multiplying more than two binomials
- Demonstrate the ability to combine like terms

#1:

Instructions: Find each product.

a) (3n - 5)(4n + 5)

b) (5m - 4)(4m + 4)

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#2:

Instructions: Find each product.

a) $$\left(2x + \frac{5}{3}\right)\left(\frac{9x}{4} + \frac{1}{5}\right)$$

b) $$\left(\frac{-11x}{3} + \frac{12}{5}\right)\left(5x + \frac{5}{2}\right)$$

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#3:

Instructions: Find each product.

a) (4m - 7n)(-4m + 4n)

b) (-x + 7y)(-4x - y)

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#4:

Instructions: Find each product.

a) (8x - 8y)(3x - 2y)

b) (3m - 5n)(-5m + 3n)

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#5:

Instructions: Find each product.

a) (3x - 3y)(8x - 5y)(2x - 2y)

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Written Solutions:

#1:

Solutions:

a) 12n^{2} - 5n - 25

b) 20m^{2} + 4m - 16

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#2:

Solutions:

a)

9x^{2} |
+ | 83x | + | 1 |

2 | 20 | 3 |

b)

-55x^{2} |
+ | 17x | + | 6 |

3 | 6 |

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#3:

Solutions:

a) -16m^{2} + 44mn - 28n^{2}

b) 4x^{2} - 27xy - 7y^{2}

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#4:

Solutions:

a) 24x^{2} - 40xy + 16y^{2}

b) -15m^{2} + 34mn - 15n^{2}

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#5:

Solutions:

a) 48x^{3} - 126x^{2}y + 108xy^{2} - 30y^{3}