Grade 10 Academic Mathematics
Unit 4 – Lesson 6
Factor a Perfect Square Trinomial and a Difference of Squares
Learning objective - Factor a difference of squares and
Perfect Square Trinomials.
Difference of Squares
Binomials where the first and last terms are perfect squares and the sign in the middle
is subtraction are called difference of squares. These binomials are actually trinomials
where the middle term is zero.
Ex. 4a2 - 16b2
Perfect Square Trinomials
Trinomials whose first and last terms are perfect squares and whose middle term is
twice the product of the square roots of the first and last terms are called perfect
square trinomials.
Ex. 4x2 + 12x + 9
Example :
1. Determine whether each of the following are perfect squares, difference of squares or
neither. Justify your answers.
a) y2 - 12y + 36
b) 4a2 - b2
c) 25y2 - 20y + 4
d) 9x2 + 3x - 6
e) 49x2 - 81y2
f) m2 + 6m + 16
g) m2 + 16
h) 4y2 + 16y + 16
I) 9x2 - 25y
Grade 10 Academic Mathematics
How to factor these:
Perfect Square Trinomials
a2 + 2ab + b2 = (a + b)2
OR
a2 - 2ab + b2 = (a - b)2
(square root of first term plus/minus square root of last term)2
Difference of Squares
a2 - b2 = (a + b)(a - b)
(square root of first term plus square root of last term)(square root of first term
minus square root of last term)
Examples :
1. Factor each of the following using the appropriate method. Be sure to remove any
common factors first.
a) 9x2 - 6x + 1
b) 49a2 - 81b2
c) 4x2 + 12x + 9
d) y2 - 12y + 36
e) 4x2 - 16y2
f) 5x2 - 20x + 20
g) 5x2 - 5
h) 16a2 - 36b2
i) 18a2 + 60ab + 50b2