Question

1. factor ( 25x^4 - 9y^4 ).

a. ( (25x^2 + 9y^2)^2 )

b. not factorable

c. ( (5x^2 + 3y^2)(5x^2 - 3y^2) )

d. ( (2x^2 + 5y^2)(2x^2 - 5y^2) )

Explanation:

Step1: Recognize difference of squares

The expression $25x^4 - 9y^4$ can be rewritten as $(5x^2)^2 - (3y^2)^2$, which fits the difference of squares form $a^2 - b^2$.

Step2: Apply difference of squares formula

Use the identity $a^2 - b^2=(a+b)(a-b)$, where $a=5x^2$ and $b=3y^2$.

$$\begin{align} (5x^2)^2 - (3y^2)^2&=(5x^2+3y^2)(5x^2-3y^2) \end{align}$$

Answer:

c. $(5x^{2}+3y^{2})(5x^{2}-3y^{2})$