Question

what is the completely factored form of $25x^4 - 16y^2$?$(5x^4 + 4y)(5x - 4y)$$(5x^3 + 4y)(5x^2 - 4y)$$(5x^2 + 4y)(5x^2 - 4y)$$25x^4 - 16y^2$done

Explanation:

Step1: Recognize difference of squares

The expression $25x^4 - 16y^2$ fits $a^2 - b^2$, where $a^2=25x^4$ and $b^2=16y^2$.

Step2: Identify $a$ and $b$

Calculate $a = \sqrt{25x^4}=5x^2$, $b=\sqrt{16y^2}=4y$.

Step3: Apply difference of squares formula

Use $a^2 - b^2=(a+b)(a-b)$. Substitute $a=5x^2$, $b=4y$.
<Expression>
$25x^4 - 16y^2=(5x^2+4y)(5x^2-4y)$
</Expression>

Answer:

C. $(5x^2 + 4y)(5x^2 - 4y)$