The document discusses factoring the difference of two squares. It explains that factoring the difference of two squares is the reverse of multiplying the sum and difference of the same two terms. An example of factoring x^2 - 9 into (x + 3)(x - 3) is provided to illustrate this process. The document then provides another example, factoring 4x^2 - 25 into (2x + 5)(2x - 5).

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)