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) 12n2 - 5n - 25
b) 20m2 + 4m - 16
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#2:
Solutions:
a)
| 9x2 | + | 83x | + | 1 |
| 2 | 20 | 3 |
b)
| -55x2 | + | 17x | + | 6 |
| 3 | 6 |
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#3:
Solutions:
a) -16m2 + 44mn - 28n2
b) 4x2 - 27xy - 7y2
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#4:
Solutions:
a) 24x2 - 40xy + 16y2
b) -15m2 + 34mn - 15n2
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#5:
Solutions:
a) 48x3 - 126x2y + 108xy2 - 30y3
