Question

factor.

1. $25x^{4}-110x^{2}+121$
2. $-x^{2}+16$

$sqrt{-1}=1$
$sqrt{16}=4$

1. $72x^{3}-242x$
2. $9x^{2}-6x+1$

Explanation:

Step1: Rewrite as perfect square trinomial

$25x^4 - 110x^2 + 121 = (5x^2)^2 - 2(5x^2)(11) + 11^2$

Step2: Apply perfect square formula

$(a-b)^2=a^2-2ab+b^2$, so:
$(5x^2 - 11)^2$

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Step1: Rearrange into difference of squares

$-x^2 + 16 = 16 - x^2 = 4^2 - x^2$

Step2: Apply difference of squares formula

$a^2-b^2=(a-b)(a+b)$, so:
$(4 - x)(4 + x)$

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Step1: Factor out greatest common factor

$\text{GCF}(72x^3,242x)=2x$, so:
$2x(36x^2 - 121)$

Step2: Rewrite as difference of squares

$36x^2 - 121 = (6x)^2 - 11^2$

Step3: Apply difference of squares formula

$a^2-b^2=(a-b)(a+b)$, so:
$2x(6x - 11)(6x + 11)$

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Step1: Rewrite as perfect square trinomial

$9x^2 - 6x + 1 = (3x)^2 - 2(3x)(1) + 1^2$

Step2: Apply perfect square formula

$(a-b)^2=a^2-2ab+b^2$, so:
$(3x - 1)^2$

Answer:

1. $\boldsymbol{(5x^2 - 11)^2}$
2. $\boldsymbol{(4 - x)(4 + x)}$
3. $\boldsymbol{2x(6x - 11)(6x + 11)}$
4. $\boldsymbol{(3x - 1)^2}$