Grade 8

2. Question…
How to factor perfect square trinomials?

3. To factor perfect square trinomials:
1. Get the square root of the first
and last terms.
2. List down the square root as
sum/difference of two terms as the
case may be.

4. Factor the following.
1.) n2 + 16n + 64 = ________
2.) 4r2 – 12r + 9 = ________
3.) 75t3 + 30t2 + 3t= ________
a.)Notice that 3t is common to all terms, thus, factoring it
out first we have: 3t(25t2 + 10t +1)
b.)Notice that 25t2 = (5t)2 and 1 = (1)2, and 10t= 2(5t)(1),
then 25t2 + 10t + 1 is a perfect square trinomial.
c.)Factoring 25t2 + 10t + 1 is (5t + 1)2, thus, the factors of
the given expression are 3t(5t + 1)2.

5. Supply the missing term to make a true
statement.
1.) m2 + 12m + 36 = (m + _____)2
2.) 16d2 – 24d + 9 = (4d - ____)2
3.) a4b2 – 6abc + 9c2 = (a2b ___ ____)2
4.) 9n2 + 30nd + 25d2 = (_____ ___ 5d)2
5.) 18h2 + 12h + 2 = 2(____ ___ ____)2
6.) 20f4 – 60f3 + 45f2 = ____(2f ___ ______)2

6. Fill in the blanks to make each expression a perfect square
trinomial.
1. x2 – 14x + ____ 6. 25x2 + 20x + ____
2. y2 + 10y + ____ 7. 36m2 - ____ + 49
3. ____ - 4a + 1 8. 225p2 + ____ + 4
4. b2 - ____ + 36 9. 81y2 + 90y + ____
5. ____ + 20m + 1 10. 64x2 - ____ + 121

7. Assignment…
Factor each completely.
1.) a2 + 6a + 9
2.) 1 + 8c + 16c2
3.) 64d2 – 16d + 1
4.) 49g2 + 56gh + 16h2
5.) 9m2 – 30mn + 25n2