Lesson 8-7 Warm-Up
ALGEBRA 1
“Factoring Special Cases” (8-7)
What is a
“perfect square
trinomial”?
Perfect Square Trinomial: a trinomial in the form of:
a2 + 2ab + b2 or a2 - 2ab + b2
In other words, the middle term is twice the product of one a and one b (actor of
the third term).
How do you
factor a “perfect
square
trinomial”?
Rule: Perfect Square Trinomials: :
a2 + 2ab + b2 = (a + b)(a + b) = (a + b)2
a2 - 2ab + b2 = (a - b)(a - b) = (a - b)2
Examples: x2 + 10x + 25 = (x + 5)(x + 5) = (x + 5)2
x2 - 10x + 25 = (x - 5)(x - 5) = (x - 5)2
ALGEBRA 1
“Factoring Special Cases” (8-7)
Tip: To recognize a perfect square trinomial:
1. The first and last terms can both be written as the product of two identical
factors.
2. The middle term is twice the product of a factor of the first terms and a factor
of the third term.
Example: 4x2 + 12x + 9
4x2 + 20x + 9
2x•2x
3•3
2x•2x
3•3
2(2x • 3) = 12x 
Area Model:
2(2x • 3) ≠ 12x
2x + 3
2x + 3
2x + 3
How can you
recognize a
perfect square
trinomial?
2x + 3
ALGEBRA 1
Factoring Special Cases
LESSON 8-7
Additional Examples
Factor m2 – 6m + 9.
m2 – 6m + 9 = m • m – 6m + 3 • 3
Rewrite first and last terms.
= m • m – 2(m • 3) + 3 • 3
Does the middle term equal
2ab? 6m = 2(m • 3)
= (m – 3)2
Write the factors as the square
of a binomial.
ALGEBRA 1
Factoring Special Cases
LESSON 8-7
Additional Examples
The area of a square is (16h2 + 40h + 25) in.2 Find the
length of a side.
16h2 + 40h + 25 = (4h)2 + 40h + 52
Write 16h2 as (4h)2
and 25 as 52.
= (4h)2 + 2(4h)(5) + 52
Does the middle term equal 2ab? 40h = 2(4h)(5)
= (4h + 5)2
Write the factors as the square of a binomial.
The side of the square has a length of (4h + 5) in.
ALGEBRA 1
“Factoring Special Cases” (8-7)
Rule: Recall that the difference of two squares is a2 - b2 . The factors of the
How do you
difference of two squares is the product of the sum and difference of a and b.
factor the
“difference of two
squares”?
a2 - b2 = (a + b)(a - b)
Examples: Factor x2 - 64
x2 - 64 = x2 - 82
(x + 8)(x - 8)
Rewrite 64 as 82 so the first and
second terms are both squared
Factor using the difference of two
squares rule
Check (using FOIL) : (x + 8)(x - 8) = x2 + 8x - 8x - 82
= x 2 - 82
= x2 - 64 
ALGEBRA 1
Factoring Special Cases
LESSON 8-7
Additional Examples
Factor a2 – 16.
a2 – 16 = a2 – 42
= (a + 4)(a – 4)
Rewrite 16 as 42.
Factor.
Check: Use FOIL to multiply.
(a + 4)(a – 4)
a2 – 4a + 4a – 16
a2 – 16
ALGEBRA 1
Factoring Special Cases
LESSON 8-7
Additional Examples
Factor 9b2 – 225.
9b2 – 225 = (3b)2 – 152
= (3b + 15)(3b –15)
Rewrite 9b2 as (3b)2 and 225 as 152.
Factor.
ALGEBRA 1
Factoring Special Cases
LESSON 8-7
Additional Examples
Factor 5x2 – 80.
5x2 – 80 = 5(x2 – 16)
= 5(x2 – 42)
Factor out the common factor of 5.
Turn the binomial into the difference of two squares.
= 5(x + 4)(x – 4) Factor (x2 – 16).
Check: Use FOIL to multiply the binomials. Then multiply by common factor.
5(x + 4)(x – 4)
5(x2 – 16)
5x2 – 80
ALGEBRA 1
Factoring Special Cases
LESSON 8-7
Lesson Quiz
Factor each expression.
1. y2 – 18y + 81
(y – 9)2
2. 9a2 – 24a + 16
(3a – 4)2
3. p2 – 169
4. 36x2 – 225
(p + 13)(p – 13)
5. 5m2 – 45
5(m + 3)(m – 3)
9(2x + 5)(2x – 5)
6. 2c2 + 20c + 50
2(c + 5)2
ALGEBRA 1