Transcript difference of two squares

6.2 Difference of 2 Squares
List all the perfect square
constants in order
1,4,9,16,25,36,49,64,81,100,121,144,169,
196,225……etc
List all the perfect square
variables
2
4
6
8
10
12
14
x , x , x , x , x , x , x ....etc
A “term” (such as 9x4)
is a Perfect Square if:
• The coefficient (9) is a perfect
square, and
• The variable has an even
number for an exponent.
• To take the square of an even
exponent divide by 2
Is this term a perfect Square?
6
4y
9
4y
6
1y
10
8y
10
25y
1
16y
156
9y
=
78
3y
•
78
3y
Factoring
the difference of two squares
Rule:
2
A
–
2
B
= (A + B)(A – B)
Ex 1: Factor:
2
9x – 25
(3x + 5 )( 3x - 5 )
Ex 2: Factor:
6
2
y – 9x
3
(y
+
3
3x)(y
- 3x)
Ex 3:Factor:
6
2
4y – 9x
3
(2y
+
3
3x)(2y
- 3x)
5x
Ex 4: Factor:
4
25x - 9
2

 3 5x  3
2

Homework
Page 268 (1-28) all
Day 2” 6.2 Difference of Two
Squares
Three Important Ideas
1.) Anytime there is a + sign with two positive
numbers you can not take the difference of
two squares.
Ex: (y2 + 25) cannot be factored.
But…..
If you have a + sign with one negative and
one positive number you can rearrange it to
look like a difference of two squares
Ex: -25+x²
x²+-25
x²-25
(x+5)(x-5)
Three Important Ideas
2.) Factor out any common terms first, then
factor as the difference of two squares if
possible
Ex : Factor:
32x2 – 50y2
2(16x2 – 25y2)
2(4x + 5y) (4x - 5y)
Ex : Factor:
9x4 + 36
9( x  4)
4
Three Important Ideas
3.) Factor completely!!! Sometimes, the
minus binomial will be another difference
of two squares. Keep factoring until it is
not another difference of two squares!
Ex: Factor
4
81x – 1
 (9x2 + 1) (9x2 – 1)
(9x² +1) (3x + 1) (3x - 1)
Ex Factor:
16x4 – y8
(4x2 + y4) (4x2 – y4)
(4x2 + y4)(2x + y2) (2x – y2)
Homework
Page 268 (30-62) even