Page 558 - Algebra 1

L E S S O N Factoring Special Products 83
Warm Up
New Concepts
1. Vocabulary A trinomial that is the square of a binomial is
(60)
called a(n) . Factor.
2.3x4 -12x (38)
Multiply. 4.(2b-3)2
(60)
3.48y2 +16y3 -56y5 (38)
5. (3x+7)(3x-7) (60)
Look for a pattern in the products. (x+1)2 =(x+1)(x+1)=x2 +2x+1 (x+2)2 =(x+2)(x+2)=x2 +4x+4 (x+3)2 =(x+3)(x+3)=x2 +6x+9 (x-1)2 =(x-1)(x-1)=x2 -2x+1 (x-2)2 =(x-2)(x-2)=x2 -4x+4
The pattern is:
Square the first term in the binomial. Square the second term in the binomial. Multiply the product of both terms by 2.
x2 +2·1x+12
x2 +2·2x+22
x2 +2·3x+32
x2 -2·1x+(-1)2 x2 -2·2x+(-2)2
Math Reasoning
Verify How can you check the products of these binomials?
Recall that a perfect-square trinomial is a polynomial that is the square of a binomial. The trinomial has the form a2 + 2ab + b2 or a2 - 2ab + b2. When squaring binomials use the following patterns:
(a+b)2 =a2 +2ab+b2
(a-b)2 =a2 -2ab+b2
Use the same patterns to factor perfect-square trinomials.
Perfect-Square Trinomials
The factored form of a perfect-square trinomial is:
a2 +2ab+b2 =(a+b)2 Example:x2 +12x+36=(x+6)2
a2 -2ab+b2 =(a-b)2 Example:x2 -12x+36=(x-6)2
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Lesson 83 543