factor using difference of squares.

Factoring ChartThis chart will help you to determine

which method of factoring to use. Type Number of Terms1. GCF 2 or more

2. Difference of Squares 2

Determine the pattern1

4

9

16

25

36

…

= 12

= 22

= 32

= 42

= 52

= 62

These are perfect squares!

You should be able to list the first 15 perfect

squares in 30 seconds…

Perfect squares1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

Review: Multiply (x – 2)(x + 2)

First terms:

Outer terms:

Inner terms:

Last terms:

Combine like terms.

x2 – 4

x -2

x

+2

x2

+2x

-2x

-4

This is called the difference of squares.

x2

+2x-2x-4

Notice the middle terms

eliminate each other!

Difference of Squares

a2 - b2 = (a - b)(a + b)or

a2 - b2 = (a + b)(a - b)

The order does not matter!!

4 Steps for factoringDifference of Squares

1. Are there only 2 terms?2. Is the first term a perfect square?3. Is the last term a perfect square?4. Is there subtraction (difference) in the

problem?If all of these are true, you can factor

using this method!!!

1. Factor x2 - 25When factoring, use your factoring table.

Do you have a GCF?

Are the Difference of Squares steps true?Two terms?

1st term a perfect square?

2nd term a perfect square?

Subtraction?

Write your answer!

No

Yes x2 – 25

Yes

Yes

Yes

( )( )5 xx + 5-

2. Factor 16x2 - 9When factoring, use your factoring table.

Do you have a GCF?

Are the Difference of Squares steps true?Two terms?

1st term a perfect square?

2nd term a perfect square?

Subtraction?

Write your answer!

No

Yes 16x2 – 9

Yes

Yes

Yes

(4x )(4x )3+ 3-

When factoring, use your factoring table.

Do you have a GCF?

Are the Difference of Squares steps true?Two terms?

1st term a perfect square?

2nd term a perfect square?

Subtraction?

Write your answer!

(9a )(9a )7b+ 7b-

3. Factor 81a2 – 49b2

No

Yes 81a2 – 49b2

Yes

Yes

Yes

Factor x2 – y2

1. (x + y)(x + y)

2. (x – y)(x + y)

3. (x + y)(x – y)

4. (x – y)(x – y)

Remember, the order doesn’t matter!

When factoring, use your factoring table.

Do you have a GCF?

3(25x2 – 4)

Are the Difference of Squares steps true?Two terms?

1st term a perfect square?

2nd term a perfect square?

Subtraction?

Write your answer! 3(5x )(5x )2+ 2-

4. Factor 75x2 – 12

Yes! GCF = 3

Yes 3(25x2 – 4)

Yes

Yes

Yes

Factor 18c2 + 8d2

1. prime

2. 2(9c2 + 4d2)

3. 2(3c – 2d)(3c + 2d)

4. 2(3c + 2d)(3c + 2d)

You cannot factor using difference of squares because there is no

subtraction!

Factor -64 + 4m2

Rewrite the problem as 4m2 – 64 so the

subtraction is in the middle!

1. prime

2. (2m – 8)(2m + 8)

3. 4(-16 + m2)

4. 4(m – 4)(m + 4)