Factoring - Difference of Squares

What is a Perfect Square

What numbers are Perfect Squares?

Squares

1 12 2 42 3 92 4 162 5 252 6 362

Perfect Squares

149162536496481100 10

8

6

4

2

x

x

x

x

x

Factoring: Difference of Squares

Count the number of terms. Is it a binomial?

Is the first term a perfect square?

Is the last term a perfect square?

Is it, or could it be, a subtraction of two perfect squares?

x2 – 9 = (x + 3)(x – 3)

The sum of squares will not factor a2+b2

Using FOIL we find the product of two binomials.

)5)(5( xx

2x x5 x5 25252 x

Rewrite the polynomial as the product of a sum and a difference.

)5)(5( xx252 x

Conditions for Difference of Squares

Must be a binomial with subtraction. First term must be a perfect square.

(x)(x) = x2

Second term must be a perfect square (6)(6) = 36

362 x

66 xx

Check for GCF.

Sometimes it is necessary to remove the GCF before it can be factored more completely.

22 455 yx 22 95 yx

yxyx 335

Removing a GCF of -1.

In some cases removing a GCF of negative one will result in the difference of squares.

162 x

161 2 x

441 xx

Difference of Squares

254 2 x

82 2 x1002 b

162 y

5252 xx

42 2 x 222 xx

PRIME! GCF. No

square.perfect anot 1st.

1001 2 b

44 yy

You Try

Factoring - Difference of Squares