Warm-up:
• Write each number as a perfect square:
(example: 16 = 42 )
1.
2.
3.
4.
25
81
36
9
Factoring Difference of Squares
Factor:
𝑥2 − 4
𝑥 2 + 0𝑥 − 4
Answer: (𝑥 + 2)(𝑥 − 2)
The middle term cancels out when we FOIL
𝑥 2 − 2𝑥 + 2𝑥 − 4
𝑥 2 + 0𝑥 − 4
𝑥2 − 4
Difference of 2 Squares
• The difference of two squares is written as:
𝑎2 − 𝑏2
– Both terms must be perfect squares
• “Perfect Square”
We multiply something by itself to get a perfect
square.
Perfect Square:
• Which ones are perfect squares?
3𝑥 2
2𝑥 2
16𝑥 2
9
36𝑥 2
36𝑥
4𝑥 2
Factoring difference of 2 squares:
𝑎2 − 𝑏2 = 𝑎 + 𝑏 𝑎 − 𝑏
Example:
Factor: 𝑥 2 − 25
𝑥 2 − 52 rewrite 25 as 52
(𝑥 + 5)(𝑥 − 5) follow the formula
Factoring difference of 2 squares:
• Example:
Factor 𝑎2 − 16 are both terms perfect squares?
𝑎2 − 42 rewrite 16 as 42
Formula: 𝑎 2 − 𝑏 2 = (𝑎 + 𝑏)(𝑎 − 𝑏)
𝑎2 − 42 = (𝑎 + 4)(𝑎 − 4)
Factored answer: (𝑎 + 4)(𝑎 − 4)
Try one…
Factor: 𝑝2 − 36