Page 392 - Algebra 1

b. Find the product of (x - 5)(x - 7). SOLUTION
(x - 5)(x - 7)
x(x - 7) = x2 - 7x -5(x - 7) = -5x + 35 x2 - 7x - 5x + 35
x2 - 12x + 35
Distribute first term in (x - 5). Distribute second term in (x - 5).
Combine the products. Simplify.
A second method of multiplying binomials is called the FOIL Method. FOIL stands for First, Outer, Inner, Last and is used as a tool to remember the steps for distributing the terms of the first binomial through the second binomial.
The FOIL Method
First, Outer, Inner, Last
(x + 2)(x + 3) First (x + 2)(x + 3) Outer (x + 2)(x + 3) Inner (x + 2)(x + 3) Last
Math Reasoning
Analyze Compare using distribution and the FOIL method to multiply binominals.
Example
3
Using the FOIL Method
a. Find the product of (2a + 5)(3a + 1).
SOLUTION
Each term of one polynomial must be multiplied by each term of the other polynomial.
(2a)(3a) = 6a2 (2a)(1) = 2a (5)(3a) = 15a
(5)(1) = 5
6a2 +2a+15a+5 6a2 +17a+5
Find the product of the First terms. Find the product of the Outer terms. Find the product of the Inner terms. Find the product of the Last terms. Add the four products.
Simplify.
b. Find the product of (8k - 1)(-3k - 5).
SOLUTION
(8k - 1)(-3k - 5) FOIL
(8k)(-3k) + (8k)(-5) + (-1)(-3k) + (-1)(-5) -24k2 - 40k + 3k + 5
-24k2 - 37k + 5
Use the FOIL method. Simplify.
Combine like terms.
Lesson 58 377