Page 127 - Math Course 2 (Book 1)

Perfect Square Trinomials

Mo. 4

Lesson 3 perfect square trinomials

Perfect square trinomials are trinomials that are
KEY CONCEPTS: the squares of binomials. Whenever you multiply a
1. Factor perfect square trinomials. binomial by itself twice, the resulting trinomial is
2. Solve equations involving perfect squares. called a perfect square trinomial.

a + 2ab + b = (a + b) 2
2
2
MO. 4 - L3a
a b
Factoring Perfect Square

Trinomials
a = 5 a

Vocabulary A-Z
Let us learn some vocabulary b = 3
b

Key Concept 25 + 15 + 15 + 9 = 64

a b
Factoring Perfect
Square Trinomials
(a + b) 2
Words if a trinomial can be written in the form a + ab + ab + b 2 a a 2 ab
2
2
2
2
2
a + 2ab + b or a – 2ab + b , then it be a + 2ab + b 2
2
2
2
factored as (a + b) or as (a – b) , 2
respectively. (5 + 3)
2
8 = 64
2
Symbols a + 2ab + b = (a + b) 2 b ab b 2
2
and
2
2
a – 2ab + b = (a + b) = (a – b) 2
2
Concept Summary
Factoring by Grouping
Number of Terms Factoring Technique Example
2
2
2
2 or more greatest common factor 3x +6x – 15x = 3x(x + 2x – 5)
2
2
2
2 difference of a – b = (a + b)(a – b) 4x – 25 = (2x + 5) (2x – 5)
squares
2
2
2
perfect square a + 2ab + b = (a + b) 2 x + 6x + 9 = (x + 3) 2
2
2
2
2
trinomial a – 2ab + b = (a – b) 2 4x – 4x + 1 = (2x – 1)
2
x + bx + c = (x + m)(x + n)
2
3 x + bx + c when m + n = b and mn = c x2 – 9x + 20 = (x – 5)(x – 4)
2
2
2
2
ax + bx + c = ax + mx + nx + c 6x – x – 2 = 6x + 3x –4x – 2
2
ax + bx + c when m + n = b and mn = ac. = 3x (2x + 1)–2(2x + 1)
Then use factoring by grouping. = (2x + 1)(3x – 2)
3xy – 6y + 5x – 10
ax + bx + ay + by
factoring by = (3xy – 6y) + (5x – 10)
4 or more = x (a + b) + y(a + b)
groupings = 3y(x – 2) + 5(x – 2)
= (a + b) (x + y)
= (x – 2) (3y + 5)
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