Factoring ax2 – c

Math 10

LEQ: How can you factor differences of two squares?

Vocabulary:-None!

Introduction

You are know going to factor a difference of squares.

What operation does difference mean?

Give me examples of squares. (Not the shape!)

The new expression you should know is:ax2 - c

Guided Notes

Have your guided notes ready to fill in.

Degree must be 2 with subtraction

The number of terms is 2

Must be able to take the square root of “a” and “c”

Steps to Factoring Success1) Take the square root of the coefficient and

the variable of the 1st term. Write your answer in your parentheses.

~Note: when you take the square root of a variable w/ exponents, just divide the exponent by 2.

2) Take the square root of the last term and write it as the last term in both parentheses

3) Make one a + and the other a – (minus)

Factoring Difference of Squares

Example: 81x2 – 36( ) ( )

√(81x2) = √(36) =

9x 9x6 6+ -

9x6

Factoring Difference of Squares

Example: x2 – 81( ) ( )

√(x2) = √(81) =

x x9 9+ -

x9

Factoring Difference of Squares

Example: 9x4 – 16q2

( ) ( )√(9x4) = √(16q2) =

3x2 3x24q 4q+ -

3x2

4q

Factoring Difference of Squares

Example: 1 – 4x2

( ) ( )√(1) = √(4x2) =

1 12x 2x+ -

12x

Factoring Difference of Squares

Example: m8 – 49( ) ( )

√(m8) = √(49) =

m4 m47 7+ -

m4

7

Factoring Difference of Squares

Example: 100x2 – 4y2

( ) ( )√(100x2) = √(4y2) =

10x 10x2y 2y+ -

10x2y

Factoring Difference of Squares

Example: x4 – 25y6

( ) ( )√(x4) = √(25y6) =

x2 x25y3 -+ 5y3

x2

5y3