Question

factor completely.

1. $16x^4 - 72x^2 + 81$
2. $x^2 + 121 + 22x$
3. $x^2 + 24x + 144$
4. $75x^3 - 60x^2 + 12x$

Explanation:

Step1: Rewrite as quadratic in $x^2$

$16x^4 - 72x^2 + 81 = (4x^2)^2 - 2(4x^2)(9) + 9^2$

Step2: Apply perfect square formula

$(4x^2 - 9)^2$

Step3: Factor difference of squares

$(4x^2 - 9) = (2x-3)(2x+3)$, so $(2x-3)^2(2x+3)^2$

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Step1: Rearrange terms

$x^2 + 22x + 121$

Step2: Apply perfect square formula

$x^2 + 2(x)(11) + 11^2 = (x+11)^2$

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Step1: Identify perfect square form

$x^2 + 24x + 144 = x^2 + 2(x)(12) + 12^2$

Step2: Apply perfect square formula

$(x+12)^2$

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Step1: Factor out GCF

$75x^3 - 60x^2 + 12x = 3x(25x^2 - 20x + 4)$

Step2: Factor quadratic inside

$25x^2 - 20x + 4 = (5x-2)^2$, so $3x(5x-2)^2$

Answer:

1. $(2x-3)^2(2x+3)^2$
2. $(x+11)^2$
3. $(x+12)^2$
4. $3x(5x-2)^2$