6.3 Trinomial Squares
• Goals: To recognize a trinomial square and
be able to factor it
• Remember to always factor out a common
factor before you see if it is a trinomial
square or not!!
Checklist to see if it is a
Trinomial Square
• Are the first and last terms perfect squares?
• Are the first and last terms positive?
• Is the middle term the product of the first
two term’s square root multiplied by 2?
Song
• Sung to the "itsy bitsy spider"
First you take the square root of terms one and three.
Double the product, then you check to see, If it matches term
two you're ready to declare The three-term trinomial is a
perfect square.
Trinomial Squares
4x2 – 20x + 25
• 4x² and 25 are perfect squares
• 4x² and 25 are positive
• The square root of 4x² is 2x and the
square root of 25 is 5. Thus (2x) (5)
is 10x then multiply it by 2 and we
get 20x which is the middle term!
Is x2 + 8x + 16
a Trinomial Square?
Yes!!
• Are the first and last terms perfect
squares?
• Are the first and last terms positive?
• Is the middle term the product of the
first two term’s square root multiplied
by 2?
Is x2 - 12x + 4
a Trinomial Square?
no
• Are the first and last terms perfect
squares?
• Are the first and last terms positive?
• Is the middle term the product of the
first two term’s square root multiplied
by 2?
Is 9x2 - 12x + 16
a Trinomial Square?
no
• Are the first and last terms perfect
squares?
• Are the first and last terms positive?
• Is the middle term the product of the
first two term’s square root multiplied
by 2?
To Factor Trinomial Squares:
• A2 + 2AB + B2  (A + B)2
• A2 - 2AB + B2  (A - B)2
Factor: x2 + 10x + 25
(x + 5)2
To Factor Trinomial Squares:
• A2 + 2AB + B2  (A + B)2
• A2 - 2AB + B2  (A - B)2
Factor: x2 - 8x + 16
(x - 4)2
To Factor Trinomial Squares:
• A2 + 2AB + B2  (A + B)2
• A2 - 2AB + B2  (A - B)2
Factor: 4x2 + 12x + 9
(2x + 3)2
To Factor Trinomial Squares:
• A2 + 2AB + B2  (A + B)2
• A2 - 2AB + B2  (A - B)2
Factor: 2x2 + 12x + 18
2(x2 + 6x + 9)
2(x + 3)2
Factor: x2 - 8x + 16
( x - 4 )2
Check your answer using FOIL
or put it in a chart
(x – 4)(x – 4)
Factor: 4x2 + 12x + 9

first term 
last term
(2x + 3)2

2
Factor: 9x2 + 30xy + 25y2

first term 
last term
(3x + 5y)2

2
Factor: 2x2 + 12x + 18
2(x2 + 6x + 9)
2(x + 3)2
Assignment:
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