Factoring Perfect Square Trinomials

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What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial. It takes the form (a + b)² = a² + 2ab + b² or (a - b)² = a² - 2ab + b².

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CCSS.HSA.APR.C.4

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Factor: x² - 4x + 4

Back

(x - 2)²

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CCSS.HSA.APR.C.4

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Factor: x² - 20x + 100

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(x - 10)²

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CCSS.HSA.APR.C.4

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Factor: x² + 18x + 81

Back

(x + 9)²

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CCSS.HSA.APR.C.4

Front

Is x² + 18x + 9 a perfect square trinomial?

Back

No

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CCSS.HSA.APR.C.4

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Factor: x² - 30x + 225

Back

(x - 15)²

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CCSS.HSA.APR.C.4

Front

What is the general form of a perfect square trinomial?

Back

The general form is a² ± 2ab + b².

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CCSS.HSA.APR.C.4

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How do you identify a perfect square trinomial?

Back

Check if the first and last terms are perfect squares and if the middle term is twice the product of the square roots of the first and last terms.

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CCSS.HSA.APR.C.4

Front

Factor: x² - 16

Back

(x - 4)(x + 4) (Note: This is a difference of squares, not a perfect square trinomial.)

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CCSS.HSA.APR.C.4

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What is the square of (x + 5)?

Back

(x + 5)² = x² + 10x + 25.

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CCSS.HSA.APR.C.4