Math 10
Ch 5 Polynomial
Name: __________________
Lesson 5-8 Factoring Perfect Square Trinomials and Difference of Squares
Warmup:
Factor:
#1 3 x 2 y + 12 x 2 y 4 − 15 x 4 y 3
2
2) x + 8 x + 15
3) 5 x 2 + 13 x + 6
Expand and Simplify
2
1) ( x − 5)
(
3) x − 3
2) ( a − 4 )( a + 4 )
) ( x + 3)
DIFFERENCE OF SQUARES
2
4) ( y + 3)
(a
2
− b 2 ) = ( a − b )( a + b )
Subtraction sign!!
The first term is a perfect square and the second term is a perfect square
When you multiply the sum and difference of 2 terms, (both are in a binomial) the product will be a DIFFERENCE OF
SQUARES.
Math 10
Ex. #1
a)
Ch 5 Polynomial
Name: __________________
Factor fully, check by expanding
x2 − 9
b)
d) x 2 + 100
x 2 − 16
c)
2 x 2 − 50
2
e) 3 x − 27
PERFECT SQUARE TRINOMIAL When you square a binomial, the result is a perfect square trinomial.
(a + b) 2 = (a+b)(a+b)
a(a+b)+b(a+b)
a2+ab+ab+b2
the first term (a2) is a perfect square.
the last term (b2) is a perfect square .
the middle term is twice the product of the 1st and last term in the original
binomial. (a)(b)(2)=2ab
a 2 + 2ab + b 2
Ex. #3
Factor, if possible.
a)
x2 + 6x + 9
c)
2 x 2 − 44 x + 242
Notes:
b)
c 2 − 18c + 81
d)
9 x 2 − 48 x + 64