Question

factor the expression $16y^4 - 64y^2 + 64$.\
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\\(\circ\\) a. $16(y^4 - 4y^2 - 4)$\
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\\(\circ\\) b. $16(y^4 - 4y^2 + 4)$\
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\\(\circ\\) c. $16(y^4 + 4y^2 + 4)$\
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\\(\circ\\) d. $16(y^4 + 4y^2 - 4)$

Explanation:

Step1: Factor out common term

Identify the greatest common factor (GCF) of all terms. The GCF of $16y^4$, $-64y^2$, and $64$ is 16.
$\frac{16y^4}{16} - \frac{64y^2}{16} + \frac{64}{16} = y^4 - 4y^2 + 4$

Step2: Verify factored form

Multiply the factored term by 16 to confirm:
$16(y^4 - 4y^2 + 4) = 16y^4 - 64y^2 + 64$

Answer:

b. $16(y^4 - 4y^2 + 4)$