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 Test:
#1:
Instructions: Find each product.
a) (3n - 5)(4n + 5)
b) (5m - 4)(4m + 4)
#2:
Instructions: Find each product.
a)
( | 2x | + | 5 | ) | ( | 9x | + | 1 | ) |
3 | 4 | 5 |
b)
( | -11x | + | 12 | ) | ( | 5x | + | 5 | ) |
3 | 5 | 2 |
#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:
Solution:
a) 12n^{2} - 5n - 25
b) 20m^{2} + 4m - 16
Solution:
a)
9x^{2} | + | 83x | + | 1 |
2 | 20 | 3 |
b)
-55x^{2} | + | 17x | + | 6 |
3 | 6 |
Solution:
a) -16m^{2} + 44mn - 28n^{2}
b) 4x^{2} - 27xy - 7y^{2}
Solution:
a) 24x^{2} - 40xy + 16y^{2}
b) -15m^{2} + 34mn - 15n^{2}
Solution:
a) 48x^{3} - 126x^{2}y + 108xy^{2} - 30y^{3}