3. Factoring: Perfect Square Trinomials
The first criteria of a
Perfect Square Trinomial
is that it must have three
terms.
4. Using FOIL we find the product
of two binomials.
(a + b)(a + b)
= a + ab + ab + b
2 2
= a + 2ab + b
2 2
5. Rewrite the perfect square
trinomial as a binomial squared.
So when you recognize this…
a + 2ab + b = (a + b)(a + b)
2 2
= ( a + b) 2
…you can write this.
6. Recognizing a Perfect Square Trinomial
x + 10 x + 25
2
• First term must be a perfect square.
(x)(x) = x2
• Last term must be a perfect square.
(5)(5) = 25
• Middle term must be twice the product
of the square root coefficient of the first
and last term. (2)(5)(1) = 10
7. What if it is a Perfect Square
Trinomial x + 10 x + 25
2
• If you have a perfect Square Trinomial
it is easy to factor:
Take the square root of the first
term.
Take the square root of the last term.
Use the sign of the middle term, put
in parenthesis and square the result.
x + 10 x + 25 = ( x + 5)
2 2
8. Recognizing a Perfect Square Trinomial
m + 8m + 16 = (m + 4)
2 2
• First term must be a perfect square.
(m)(m) = m2
• Last term must be a perfect square.
(4)(4) = 16
• Middle term must be twice the product
of the square root coefficient of the first
and last term.
(2)(4)(1) = 8
9. Recognizing a Perfect Square Trinomial
p − 18 p + 81= ( p − 9)
2 2
• First term must be a perfect square.
(p)(p) = p2
• Last term must be a perfect square.
Signs must match!
(9)(9) = 81
• Middle term must be twice the product
of the coefficient of the first and last
term.
(2)(9)(1) = 18p
10. Recognizing a Perfect Square Trinomial
Not a Perfect
121 p + 110 p + 100
2
Square
• First term must be a perfect square.
2 Trinomial!
(11p)(11p) = 121p
• Last term must be a perfect square.
(10)(10) = 100
• Middle term must be twice the product of the
first and last term.
(2)(10)(11p) = 220p
11. Perfect Square Trinomial Y/N
r − 8r + 16 Yes ( r − 4)
2 2
49 p − 28 p + 4 Yes ( 7 p − 2)
2 2
49 s − 42 st + 36t No
2 2
4m + 4mn + n Yes ( 2m + n )
2 2 2
d + 50d + 225 No
2
