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This pdf includes the following topics:-

Factoring Chart

Determine the pattern

Difference of Squares

4 Steps for factoring Difference of Squares

Factoring Chart

Determine the pattern

Difference of Squares

4 Steps for factoring Difference of Squares

1.
Notes 8.5

Factoring using

difference of squares.

Factoring using

difference of squares.

2.
Factoring Chart

This chart will help you to determine

which method of factoring to use.

Type Number of Terms

1. GCF 2 or more

2. Difference of Squares 2

This chart will help you to determine

which method of factoring to use.

Type Number of Terms

1. GCF 2 or more

2. Difference of Squares 2

3.
Determine the pattern

1 = 12 These are perfect squares!

4 = 22 You should be able to list

9 = 32 the first 15 perfect

16 = 42 squares in 30 seconds…

25 = 52

Perfect squares

36 = 62 1, 4, 9, 16, 25, 36, 49, 64, 81,

… 100, 121, 144, 169, 196, 225

1 = 12 These are perfect squares!

4 = 22 You should be able to list

9 = 32 the first 15 perfect

16 = 42 squares in 30 seconds…

25 = 52

Perfect squares

36 = 62 1, 4, 9, 16, 25, 36, 49, 64, 81,

… 100, 121, 144, 169, 196, 225

4.
Review: Multiply (x – 2)(x + 2)

Notice the

First terms: x2 middle terms

eliminate

x -2

Outer terms: +2x each other!

Inner terms: -2x

Last terms: -4

x x2 -2x

Combine like terms.

x2 – 4 +2 +2x -4

This is called the difference of squares.

Notice the

First terms: x2 middle terms

eliminate

x -2

Outer terms: +2x each other!

Inner terms: -2x

Last terms: -4

x x2 -2x

Combine like terms.

x2 – 4 +2 +2x -4

This is called the difference of squares.

5.
Difference of Squares

2 2

a - b = (a - b)(a + b)

or

2 2

a - b = (a + b)(a - b)

The order does not matter!!

2 2

a - b = (a - b)(a + b)

or

2 2

a - b = (a + b)(a - b)

The order does not matter!!

6.
4 Steps for factoring

Difference 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!!!

Difference 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!!!

7.
1. Factor x2 - 25

When factoring, use your factoring table.

Do you have a GCF? No

Are the Difference of Squares steps true?

Two terms? Yes x2 – 25

1st term a perfect square? Yes

2nd term a perfect square? Yes

Subtraction? Yes ( x + 5 )(x - 5 )

Write your answer!

When factoring, use your factoring table.

Do you have a GCF? No

Are the Difference of Squares steps true?

Two terms? Yes x2 – 25

1st term a perfect square? Yes

2nd term a perfect square? Yes

Subtraction? Yes ( x + 5 )(x - 5 )

Write your answer!

8.
2. Factor 16x2 - 9

When factoring, use your factoring table.

Do you have a GCF? No

Are the Difference of Squares steps true?

Two terms? Yes 16x2 – 9

1st term a perfect square? Yes

2nd term a perfect square? Yes

Subtraction? Yes (4x + 3 )(4x - 3 )

Write your answer!

When factoring, use your factoring table.

Do you have a GCF? No

Are the Difference of Squares steps true?

Two terms? Yes 16x2 – 9

1st term a perfect square? Yes

2nd term a perfect square? Yes

Subtraction? Yes (4x + 3 )(4x - 3 )

Write your answer!

9.
3. Factor 81a2 – 49b2

When factoring, use your factoring table.

Do you have a GCF? No

Are the Difference of Squares steps true?

Two terms? Yes 81a2 – 49b2

1st term a perfect square? Yes

2nd term a perfect square? Yes

Subtraction? Yes (9a + 7b)(9a - 7b)

Write your answer!

When factoring, use your factoring table.

Do you have a GCF? No

Are the Difference of Squares steps true?

Two terms? Yes 81a2 – 49b2

1st term a perfect square? Yes

2nd term a perfect square? Yes

Subtraction? Yes (9a + 7b)(9a - 7b)

Write your answer!

10.
Factor x 2 – y 2

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!

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!

11.
4. Factor 75x2 – 12

When factoring, use your factoring table.

Do you have a GCF? Yes! GCF = 3

3(25x2 – 4)

Are the Difference of Squares steps true?

Two terms? Yes 3(25x2 – 4)

1st term a perfect square? Yes

2nd term a perfect square? Yes

Subtraction? Yes

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

When factoring, use your factoring table.

Do you have a GCF? Yes! GCF = 3

3(25x2 – 4)

Are the Difference of Squares steps true?

Two terms? Yes 3(25x2 – 4)

1st term a perfect square? Yes

2nd term a perfect square? Yes

Subtraction? Yes

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

12.
Factor 18c 2 + 8d 2

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!

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!

13.
Factor -64 + 4m2

1. prime

2. (2m – 8)(2m + 8)

3. 4(-16 + m2)

4. 4(m – 4)(m + 4)

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)

Rewrite the problem as

4m2 – 64 so the

subtraction is in the

middle!