MCF3M
Unit 2, Lesson 2
Factoring: Difference of Squares and Perfect
Squares
Warm-up. Factor the following :
𝑥 2 − 6𝑥 − 16
6𝑥 2 − 9𝑥
3𝑥 2 + 2𝑥 − 8
3𝑥 2 + 𝑥 − 4
Difference of Squares
We have already looked at difference of squares.
Factor each of the following:
a) 𝑥 2 − 16
b) 𝑥 2 − 100
c) 9𝑥 2 − 4
d) 3𝑥 2 − 12
Here are some more “challenging” difference of squares.
𝑥 4 − 16
𝑥8 − 1
Perfect Squares
Factor the following: 4𝑥 2 + 12𝑥 + 9
(𝑥 + 3)2 − 1
(𝑎 − 𝑏)2 − 100
MCF3M
Unit 2, Lesson 2
The above is a perfect square. Expand each of the following to see what perfect squares look like:
a) (x + 2)2
b) (x – 4)2
c) (5x + 3)2
Sometimes it is helpful to recognize a perfect square trinomial. (will be important when we start completing the
square). However, they can always be factored as general trinomials as well (using decomposition) provided the
numbers are not too large.
Factor the following:
a) 𝑥 2 + 10𝑥 + 25
b) 4𝑥 2 − 4𝑥 + 1
c) 9𝑥 2 + 30𝑥 + 25
Complete the blank in each expression below:
a) (𝑥 + 3)2 = x2 + _____x + 9
b) (𝑥 − 4)2 = x2 + _____x + 16
c) (𝑥 + _____)2 = x2 + _____x + 25
d) (𝑥 − _____)2 = x2 - 8x + ________
MCF3M
Unit 2, Lesson 2
Factoring : Difference of Squares and Perfect Squares
1. Text page 105 #1 – 2, 4
2. Factor the following:
a) 𝑥 6 − 10 000
b) (2𝑦 − 2)2 − 9
c) 2𝑥 2 − 32
3. Complete the blanks in each expression below. Check your answer by expanding.
a) (2𝑥 + 3)2 = _______x2 + _____x + 9
b) (𝑥 + ______)2 = x2 + 2x + _______
c) (𝑥 − ______)2 = x2 - _____x + 36
d) (𝑥 + ______)2 = x2 + 20x + _______
4. Text page 106 #9