Perfect Square Trinomials

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Notes

Perfect Square Formula

Questions & Answers

Factor the Following

$1)$ $x^{2} + 4 x + 4$
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The answer is $(x + 2)^{2}$

$2)$ $x^{2} - 6 x + 9$
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The answer is $(x - 3)^{2}$

$3)$ $x^{2} + 8 x + 16$
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The answer is $(x + 4)^{2}$

$4)$ $x^{2} - 10 x + 25$
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The answer is $(x - 5)^{2}$

$5)$ $4 x^{2} + 12 x + 9$
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The answer is $(2 x + 3)^{2}$

$6)$ $9 x^{2} + 6 x + 1$
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The answer is $(3 x + 1)^{2}$

$7)$ $x^{2} - 2 x + 1$
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The answer is $(x - 1)^{2}$

$8)$ $x^{2} - 12 x + 36$
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The answer is $(x - 6)^{2}$

$9)$ $x^{2} - 20 x + 100$
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The answer is $(x - 10)^{2}$

$10)$ $x^{2} - 14 x + 49$
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The answer is $(x - 7)^{2}$

Challenge Problem

$11)$ Simplify $\sqrt{54 - 14 \sqrt{5}}$
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The answer is $7 - \sqrt{5}$

See Related Pages

$∙ Factoring Calculator$
$(Symbolab.com)$

$∙ Factoring out a GCF$
$3 x y z^{2} + x^{2} y^{2} z + 9 x^{3} y = x y (3 z^{2} + x y z + 9 x^{2}) \dots$

$∙ Factoring Trinomials with a = 1$
$x^{2} + 7 x + 12 = (x + 3) (x + 4) \dots$

$∙ Factoring Trinomials with a \neq 1$
$3 x^{2} + 11 x + 6 = (3 x + 2) (x + 3) \dots$

$∙ Factoring with u-substitution$
$x^{4} + 5 x^{2} + 6 = u^{2} + 5 u + 6 \dots$

$∙ Difference of Two Squares$
$x^{2} - 16 = (x + 4) (x - 4) \dots$

$∙ Sum/Difference of Two Cubes$
$x^{3} - 8 = (x - 2) (x^{2} + 2 x + 4) \dots$

$∙ Factor by Grouping$
$8 x^{3} - 4 x^{2} - 6 x + 3 = (4 x^{2} - 3) (2 x - 1) \dots$

$∙ Solving Quadratic Equations by Factoring$
$x^{2} + 10 x - 24 = 0 \dots$

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