Page 406 - Algebra 1

The product of a sum and difference of two binomials (a - b)(a + b) = a2 - b2 produces the difference of two squares.
Special Product of Binomials
Pattern
(a+b)2 =a2 +2ab+b2 (a-b)2 =a2 -2ab+b2
(x+5)2 =x2 +10x+25 (2x-4)2 =4x2 -16x+16
Square of a Binomial Example
Sum and Difference
Pattern Example
(a+b)(a-b)=a2 -b2 (3x-2)(3x+2)=9x2 -4
Example
1
Squaring Binomials in the Form (a + b)2
a. Find the product: (x + 2)2. SOLUTION
(a+b)2 =a2 +2ab+b2
(x + 2)2 = (x)2 + 2(x)(2) + 22
= x2 + 4x + 4
b. Find the product: (2x + 4)2. SOLUTION
(a+b)2 =a2 +2ab+b2
(2x + 4)2 = (2x)2 + 2(2x)(4) + 42
Writethepattern. Apply the pattern. Simplify.
Writethepattern. Apply the pattern. Simplify.
= 4x2 + 16x + 16
Squaring Binomials in the Form (a - b)2
Example
2
a. Find the product: (x - 8)2. SOLUTION
(a-b)2 =a2 -2ab+b2
(x - 8)2 = (x)2 - 2(x)(8) + (8)2
= x2 - 16x + 64
b. Find the product: (2x - 7)2. SOLUTION
(a-b)2 =a2 -2ab+b2
(2x - 7)2 = (2x)2 - 2(2x)(7) + (7)2
= 4x2 - 28x + 49
Writethepattern. Apply the pattern. Simplify.
Writethepattern. Apply the pattern. Simplify.
Caution
(x-5)2 ≠x2 +25
Remember to either use the pattern for squaring binomials or use the FOIL method.
(x-5)2 =(x-5)(x-5) =x2 -10x+25
Lesson 60 391