Question

factor the polynomial. 36b^4 - 25t^2 select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. 36b^4 - 25t^2 = (type your answer in factored form. factor completely.) b. the polynomial is prime.

Explanation:

Step1: Recognize difference - of - squares

The expression $36b^{4}-25t^{2}$ is in the form $a^{2}-b^{2}$, where $a = 6b^{2}$ and $b = 5t$ since $(6b^{2})^{2}=36b^{4}$ and $(5t)^{2}=25t^{2}$.

Step2: Apply difference - of - squares formula

The difference - of - squares formula is $a^{2}-b^{2}=(a + b)(a - b)$. Substituting $a = 6b^{2}$ and $b = 5t$ into the formula, we get $(6b^{2}+5t)(6b^{2}-5t)$.

Answer:

A. $(6b^{2}+5t)(6b^{2}-5t)$