6.3 Trinomial Squares
What is a trinomial square?
• The square of a binomial
–Example:
– 𝑥 + 3 2 = x 2 + 6x + 9
2
2
– 𝑥 − 3 = x − 6x + 9
Recognizing a Trinomial Square
• Two of the terms must be squares (the
first and last)
• There CANNOT be a minus sign in the
very beginning or the end (before last
number)
• If we multiply the square root of the first
term with the square root of the last term
and multiply that by 2 we should get the
middle term!
Tell whether each is a trinomial square.
x  8 x  16
2
• Are the first and last terms squares?
Yes
• There is not a minus sign in the very
beginning or the end
Yes
• If we multiply the square root of the first
term with the square root of the last term
and multiply that by 2 we should get the
middle term!
Yes (𝑥 ∙ 4 ∙ 2 = 8𝑥)
Tell whether each is a trinomial square.
x  10 x  25
2
• Are the first and last terms squares?
Yes
• There is not a minus sign in the very
beginning or the end
Yes
• If we multiply the square root of the first
term with the square root of the last term
and multiply that by 2 we should get the
middle term!
Yes (𝑥 ∙ 5 ∙ 2 = 10𝑥)
Tell whether each is a trinomial square.
x  12 x  4
2
• Are the first and last terms squares?
Yes
• There is not a minus sign in the very
beginning or the end
Yes
• If we multiply the square root of the first
term with the square root of the last term
and multiply that by 2 we should get the
middle term!
No (𝑥 ∙ 2 ∙ 2 = 4𝑥 ≠≠ 12𝑥)
Tell whether each is a trinomial square.
2
16𝑎 − 56𝑎𝑏 + 49𝑏
2
• Are the first and last terms squares?
Yes
• There is not a minus sign in the very beginning or
the end
Yes
• If we multiply the square root of the first term
with the square root of the last term and multiply
that by 2 we should get the middle term!
Yes (4a ∙ 7𝑏 ∙ 2 = 56𝑎𝑏)
Factoring a Trinomial Square
a  2ab  b  (a  b)
2
2
2
a  2ab  b  (a  b)
2
2
2
ALWAYS FACTOR OUT
COMMON FACTORS FIRST!!!!
Steps
1. Decide if the answer will be + or –
2. If the signs in the problem are:
+, + then the answer is (+)
 - , + then the answer is (-)
3. Take the square root of the first term and
put it in the beginning
4. Take the square root of the last term and put
it at the end
5. Write an exponent of 2 at the end of the
parenthesis.
Factor.
x  6x  9
2
Factor.
x  14 x  49
2
Factor.
16a  40ab  25b
2
2
Factor
1. 49𝑝2 − 28𝑝 + 4
2. 100𝑏 2 − 180𝑏 + 81
Factor.
27 m  72mn  48n
2
2
Factor.
x  4x  4x
3
2
Exit Ticket
• 𝑥 2 + 2𝑥 + 1
• 25𝑥 2 − 70𝑥 + 49
• 48𝑚2 + 120𝑚𝑛 + 75𝑛2
Assignment
• Pg.