Question

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

Explanation:

Step1: Identify common factor

The terms $16y^4$, $-64y^2$, and $64$ share a common factor of 16.

Step2: Factor out the common factor

Divide each term by 16:
$$\frac{16y^4}{16} - \frac{64y^2}{16} + \frac{64}{16} = y^4 - 4y^2 + 4$$
Combine with the factored out 16: $16(y^4 - 4y^2 + 4)$

Answer:

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