Section 6.4
Recall that there are three special product formulas:
The Product of a Binomial Squared is a Perfect
Square Trinomial
(a + b)2 = (a + b)(a + b) = a2 + 2ab + b2
(a – b)2 = (a – b)(a – b) = a2 – 2ab + b2
The Product of a Sum and Difference is a
Difference of Two Perfect Squares
(a + b)(a – b) = a2 – b2
Since factoring is the reverse of multiplication, we
can reverse these formulas:
The Factors of a Perfect Square Trinomial are
Binomials Squared
a2 + 2ab + b2 = (a + b)2
a2 – 2ab + b2 = (a – b)2
The Factors of a Difference of Two Perfect Squares
are Sum and Difference Binomials
a2 – b2 = (a + b)(a – b)
The Difference of Two Squares
Factor : 16x2 – 25.
We can see that the first term is a perfect square,
and the last term is also.
This fact becomes even more obvious if we rewrite
the problem as:
= (4x)2 – (5)2
The first term is the square of the quantity 4x, and
the last term is the square of 5.
The completed problem looks like this:
16x2 – 25 = (4x)2 – (5)2
= (4x + 5)(4x – 5)
To check our results, we can multiply:
(4x + 5)(4x – 5) = 16x2 + 20x – 20x – 25
= 16x2 – 25
Perfect Square Trinomials
Factor
25x2 – 60x + 36.
We notice that the first and last terms are the
perfect squares (5x)2 and (6)2.
Factor
25x2 – 60x + 36.
Step 1:
This is a perfect square trinomial
Rewrite as (5x)2 – 2(5x)(6) + 62
Step 2:
Recognize the special factoring formula
for a perfect square trinomial:
a2 –
Step 3:
2ab
+ b2 = (a – b)2
(5x)2 – 2(5x)(6) + 62 = (5x – 6) 2
We can check this my multiplying:
(5x – 6)2 = (5x – 6)(5x – 6)
= 25x2 – 30x – 30x + 36
= 25x2 – 60x + 36
The trinomial, 5x2 – 60x + 36
 is a perfect square trinomial

has factors of (5x – 6)(5x – 6)
OR (5x – 6)2.
Factoring Out A
Greatest Common Factor
Factor:
6x2 + 24x + 24.
= 6 (x2 + 4x + 4)
Factor out a GCF
= 6 [x2 + 2(2x) + 22 ]
Recognize the perfect square trinomial
= 6 (x+2) 2
Recall : a2 + 2ab + b2 = (a + b)2
Apply the formula
We can check this by multiplying:
6 (x+2) 2 = 6 (x+2) (x+2)
= 6 (x2 +4x + 4)
= 6x2 + 24x + 24
The trinomial, 6x2 + 24x + 24, has factors of
6(x + 2)(x+2) OR 6(x + 2)2
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Section 6.4
Pages Pages 449-452
# 1, 7, 19, 29, 43, 49, 63