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
FOIL Practice Test:

#1:

Instructions: Find each product.

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

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

#2:

Instructions: Find each product.

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

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

#3:

Instructions: Find each product.

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

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

#4:

Instructions: Find each product.

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

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

#5:

Instructions: Find each product.

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

Written Solutions:

#1:

Solutions:

a) 12n2 - 5n - 25

b) 20m2 + 4m - 16

#2:

Solutions:

a)

 9x2 + 83x + 1 2 20 3

b)

 -55x2 + 17x + 6 3 6

#3:

Solutions:

a) -16m2 + 44mn - 28n2

b) 4x2 - 27xy - 7y2

#4:

Solutions:

a) 24x2 - 40xy + 16y2

b) -15m2 + 34mn - 15n2

#5:

Solutions:

a) 48x3 - 126x2y + 108xy2 - 30y3