### Chapter 7, Section 3

```Special Factoring
The Difference of Squares
Difference of Squares
x2 – y2 = (x + y)(x – y)
Special Factoring
EXAMPLE 1
Factoring Differences of Squares
Factor each polynomial.
(a)
2n2 – 50
7.3 Special Factoring
EXAMPLE 1
Factoring Differences of Squares
Factor each polynomial.
(b)
9g2 – 16
(c)
4h2 – (w + 5)2
Special Factoring
Caution
CAUTION
Assuming no greatest common factor except 1, it is not possible to
factor (with real numbers) a sum of squares, such as x2 + 16.
Special Factoring
EXAMPLE 2
Factoring Perfect Square Trinomials
Factor each polynomial.
(a)
9g2 – 42g + 49
Special Factoring
EXAMPLE 2
Factoring Perfect Square Trinomials
Factor each polynomial.
(b)
25x2 + 60xy + 64y2
Special Factoring
EXAMPLE 2
Factoring Perfect Square Trinomials
Factor each polynomial.
(d)
c2 – 6c + 9 – h2
Special Factoring
Difference of Cubes
Difference of Cubes
x3 – y3 = (x – y)(x2 + xy + y2)
Special Factoring
Sum of Cubes
Sum of Cubes
x3 + y3 = (x + y)(x2 – xy + y2)
Sec 7.3 - 9
Special Factoring
EXAMPLE 3
Factoring Difference of Cubes
Factor each polynomial. Recall, x3 – y3 = (x – y)(x2 + xy + y2).
(a)
a3 – 125
Special Factoring
EXAMPLE 4
Factoring Sums of Cubes
Factor each polynomial. Recall, x3 + y3 = (x + y)(x2 – xy + y2).
(a)
n3 + 8
(b)
64v3 + 27g3
Special Factoring
EXAMPLE 3
Factoring Difference of Cubes
Factor each polynomial. Recall, x3 – y3 = (x – y)(x2 + xy + y2).
(b)
8g3 – h3
Special Factoring
EXAMPLE 3
Factoring Difference of Cubes
Factor each polynomial. Recall, x3 – y3 = (x – y)(x2 + xy + y2).
(c)
64m3 – 27n3
Special Factoring
EXAMPLE 4
Factoring Sums of Cubes
Factor each polynomial. Recall, x3 + y3 = (x + y)(x2 – xy + y2).
(c)
2k3 + 250 =