Factoring Difference of Squares

1. FACTORING
The Difference of Two Squares

2. Review
𝑥 + 3 𝑥 − 3 =

3. Review
F O I L
𝑥 + 3 𝑥 − 3 = 𝑥2
− 3𝑥 + 3𝑥 + 9

4. Review
F O I L
𝑥 + 3 𝑥 − 3 = 𝑥2
− 3𝑥 + 3𝑥 + 9
cancels out

5. Review
F O I L
𝑥 + 3 𝑥 − 3 = 𝑥2
− 3𝑥 + 3𝑥 − 9 = 𝑥2
− 9
cancels out

6. Factoring the difference of two squares is the reverse
of multiplying the sum and the difference of the same
two terms.
Multiply: 𝑥 + 3 𝑥 − 3 = 𝑥2 − 9
Factor: 𝑥2
− 9 = (𝑥 + 3)(𝑥 − 3)

7. Factoring the Difference of Two Square
Example:
𝑥2 − 9 =

8. Factoring the Difference of Two Square
Example:
𝑥2 − 9 = ( + )( − )

9. Factoring the Difference of Two Square
Example:
𝑥2 − 9 = ( + )( − )
𝑥2

10. Factoring the Difference of Two Square
Example:
𝑥2 − 9 = ( 𝑥 + )( 𝑥 − )
𝑥2 = 𝑥

11. Factoring the Difference of Two Square
Example:
𝑥2 − 9 = ( 𝑥 + )( 𝑥 − )
9

12. Factoring the Difference of Two Square
Example:
𝑥2 − 9 = ( 𝑥 + 3) (𝑥 −3)
9 = 3

13. Factoring the Difference of Two Square
Example:
𝑥2 − 9 = ( 𝑥 + 3)( 𝑥 − 3)

14. Factoring the Difference of Two Square
Example:
4𝑥2 − 25 =

15. Factoring the Difference of Two Square
Example:
4𝑥2 − 25 = ( + )( − )

16. Factoring the Difference of Two Square
Example:
4𝑥2 − 25 = ( + )( − )
4𝑥2 =

17. Factoring the Difference of Two Square
Example:
4𝑥2 − 25 = ( 2𝑥 + )( 2𝑥 − )
4𝑥2 = 2𝑥

18. Factoring the Difference of Two Square
Example:
4𝑥2 − 25 = ( 2𝑥 + )( 2𝑥 − )
25 =

19. Factoring the Difference of Two Square
Example:
4𝑥2 − 25 = ( 2𝑥 + 5)(2𝑥 − 5)
25 = 5

20. Factoring the Difference of Two Square
Example:
4𝑥2 − 25 = ( 2𝑥 + 5)( 2𝑥 − 5)