Factoring Perfect Square Trinomials - MathBitsNotebook(A1

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A1Side Factoring Perfect Square TrinomialsMathBitsNotebook.com Topical Outline | Algebra 1 Outline | MathBits' Teacher Resources Terms of Use Contact Person: Donna Roberts divider
We encountered perfect square trinomials under multiplying polynomials. Now, we will put them to work while factoring.
Squaring a binomial creates a perfect square trinomial: (a + b)2 (a - b)2
(a + b)2 = a2 + 2ab + b2 (a - b)2 = a2 - 2ab + b2

What we need to do now, is to "remember" these patterns so that we can be on the look-out for them when factoring.

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Notice the Pattern of the middle term: The middle term is twice the product of the binomial's first and last terms. (a + b)² middle term +2ab (a - b)² middle term -2ab In (a - b), the last term is -b.
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expin1 Factor: x2 + 12x + 36

Solution: Does this fit the pattern of a perfect square trinomial? Yes. Both x2 and 36 are perfect squares. And 12x is twice the product of x and 6.

Since all signs are positive, the pattern is (a + b)2 = a2 + 2ab + b2. Let a = x and b = 6.

Answer: (x + 6)2 or (x + 6)(x + 6)
expin2 Factor: 9a2 - 6a + 1

Solution: Does this fit the pattern of a perfect square trinomial? Yes. Both 9a2 and 1 are perfect squares. And 6a is twice the product of 3a and 1.

Since the middle term is negative, the pattern is (a - b)2 = a2 - 2ab + b2. Let a = 3a and b = 1.

Answer: (3a - 1)2 or (3a - 1)(3a - 1)
expin3 Factor: (m + n)2 + 12(m + n) + 36

Solution: This is a sneaky one! Do NOT start by removing the parentheses. Look at the pattern, instead. . Does this fit the pattern of a perfect square trinomial? Yes. Both (m + n)2 and 36 are perfect squares. And 12(m + n) is twice the product of (m + n) and 6.

Since the middle term is positive, the pattern is (a + b)2 = a2 + 2ab + b2. Let a = (m + n) and b = 6.

Answer: ((m + n) + 6)2 or (m + n + 6)2

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expin2 Factor: x2 + 4x + 4 using Algebra Tiles
KEY: algebratileskey See more about Algebra Tiles.
Place the x2 tile, 4 x-tiles and 4 1-tiles in the grid.

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 Fill the outside sections of the grid with x-tiles and 1-tiles that complete the pattern. at5
The algebra tiles show that trinomial is a perfect square trinomial, (x + 2)2.

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Topical Outline | Algebra 1 Outline | MathBitsNotebook.com | MathBits' Teacher Resources Terms of Use Contact Person: Donna Roberts

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