Download Factor Special Products (9

Factor Special Products (9.7)
Perfect Square Trinomials are Trinomials that can factor into:
Perfect Square Trinomial = (Binomial)2
**Factor like normal, if you get the same binomial for both—write it as (Binomial)2
Factor
Ex. x2 + 6x + 9 = (
)(
)=
Ex. x2 – 10x + 25 = (
)(
)=
Ex. 9x2 – 12x + 4 = (
)(
)=
Ex. 4x2 + 4xy + y2 = (
)(
)=
Factoring Binomial
Let’s see if we can factor binomials in the same way:
Ex.
x2 – 9
a = _______
b = ________
c = ________
Think: What 2 numbers multiply to equal _____ that also add to equal _______
_______ • ________ = ________
Ex.
x2 – 9 = (
)(
_______ + _______ = _______
)
**Notice that the two binomial are exactly the same, but with different signs because when opposites are
added they = 0 so there is no “b”.
1
The ONLY binomial that can be factored into a (binomial) (binomial) is “The Difference of 2 Squares”
Perfect Square
x2 – 9
Perfect Square
Subtraction


There MUST be SUBTRACTION between the two terms
Each term is a Perfect Square (can be made by a number times itself)
Examples of perfect squares:
4→ 2•2=4
9→ 3•3=9
36 → 6 • 6 = 36
x2 → x • x = x2
4m2 → 2m • 2m = 4m2
Difference of 2 square = (Sum) (Difference) = (r + s) (r – s)
Factor
Ex. x2 – 16 = (
)(
)
Ex. 25x2 – 36 = (
)(
)
Ex. x2 – 49y2 = (
)(
)
Ex. 2x2 – 25
Ex. 4x2 + 49
2