Page 407 - Algebra 1

Example
3
Finding Products in the Form (a + b)(a - b)
a. Find the product: (x + 3)(x - 3). SOLUTION
(a+b)(a-b)=a2 -b2
(x + 3)(x - 3) = (x)2 - (3)2
= x2 - 9
Writethepattern. Apply the pattern. Simplify.
b. Find the product: (5x + 4)(5x - 4). SOLUTION
(a+b)(a-b)=a2 -b2
(5x + 4)(5x - 4) = (5x)2 - (4)2
= 25x2 - 16 Mental Math
Writethepattern. Apply the pattern. Simplify.
Example
4
a. Use mental math to find 392. To use mental math, remember to use the special, product patterns.
SOLUTION
(40 - 1)2
= 402 - 2(40)(1) + (1)2 = 1600 - 80 + 1
= 1521
Write 392 as a square of binomial. Apply the pattern.
Simplify.
b. Use mental math to find the product of 16 · 24. To use mental math, remember to use the special product patterns.
SOLUTION
(20 - 4)(20 + 4) = 202 - 42 Write 16 · 24 as the product of the difference and the sum.
= 400 - 16 = 384
Simplify.
Application: Gardening
Example
5
Roberto has a garden in the shape of a parallelogram. It has a height of (x - 2) and a base length of (x + 2). Find the area of Roberto’s garden.
Math Reasoning
Write How could Roberto check his work?
392 Saxon Algebra 1
SOLUTION
A = bh
= (x - 2)(x + 2) = (x)2 - (2)2
= x2 - 4
Write as the product of difference and sum. Simplify.