Question

factor the following binomial completely. 36m² - 25/9 select the correct choice below and fill in any answer boxes within your choice. a. 36m² - 25/9 = (factor completely. use integers or fractions for any numbers in the expression.) b. the polynomial is prime.

Explanation:

Step1: Recognize difference - of - squares form

The given binomial $36m^{2}-\frac{25}{9}$ can be written as $(6m)^{2}-(\frac{5}{3})^{2}$, which is in the form $a^{2}-b^{2}$.

Step2: Apply difference - of - squares formula

The difference - of - squares formula is $a^{2}-b^{2}=(a + b)(a - b)$. Here, $a = 6m$ and $b=\frac{5}{3}$. So, $(6m)^{2}-(\frac{5}{3})^{2}=(6m+\frac{5}{3})(6m - \frac{5}{3})$.

Answer:

A. $36m^{2}-\frac{25}{9}=(6m+\frac{5}{3})(6m - \frac{5}{3})$