Algebra 1
Mr. Gallo
I. Perfect Square Trinomials
Recall: The Square of a Binomial
The SQUARE
term plus
of a binomial is the SQUARE of the FIRST
TWICE
the PRODUCT of the terms plus the
SQUARE of the LAST term.
a  b
2
 a 2  2ab  b 2
a  b
2
 a 2  2ab  b 2
Therefore something like 4 x 2  12 x  9 , can be factored
to be
 2 x  3
2
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How to recognize perfect square trinomials:
1.) The FIRST
and
LAST
terms are perfect squares!
2.) The SECOND term is twice the product of their SQUARE
roots.
Example: What is the factored form of x 2  8 x  16 ?
a  1  12
c  16  42
b  2 1 4   8
x 2  8 x  16   x  4  x  4 
x 2  8 x  16   x  4 
2
Example: What is the factored form of x 2  14 x  49
a  1  12
c  49  7 2
b  2 1 7   14
Since b is negative, we need to use the
negative square root of c.
x 2  14 x  49   x  7  x  7 
x 2  14 x  49   x  7 
2
2
2
Example: What is the factored form of 9 x  30 x  25?
a  9  32
c  25  52
Since b is negative, we need to use the
negative square root of c.
b  2  3 5   30
9 x 2  30 x  25   3 x  5  3 x  5 
9 x 2  30 x  25   3 x  5 
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II. The Difference of Two Squares
Recall: Product of a Sum and Difference
The PRODUCT
of a pair of binomials that is a SUM and a
DIFFERENCE of the same two terms is the DIFFERENCE
______________
of their SQUARES
.
 a  b  a  b  
a 2  b2
Therefore something like 4 x 2  9 , can be factored to be
 2 x    3
2
2

 2 x  3 2 x  3
3
Example: What is the factored form of x 2  49?
x 2  49 

x 2  49


x 2  49   x  7  x  7 
Example: What is the factored form of 9 x 2  25?
9 x 2  25 

9 x 2  25


9 x 2  25   3 x  5  3 x  5 
Example: What is the factored form of
16 x 2  100 ?
THERE IS NO SUM OF SQUARES!!!!
16 x 2  100 is PRIME
Homework: p.549 #14-36 even
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