Chapter 6.7, Problem 64HP

To determine

To Choose: The unit factor that represents the length and the width of the rectangle.

Answer to Problem 64HP

Thecorrect option is

Explanation of Solution

Given:

The area of the rectangle is $25a^4-16b^2$ .

Calculation:

Consider the area of the rectangle is,

  $25a^4-16b^2$

Consider the identity,

  $a^2-b^2=\left(a+b\right)\left(a-b\right)$

Then, the length and the breadth of the rectangle is,

  $\begin{array}{c}25a^4-16b^2={\left(5a^2\right)}^2-{\left(4b\right)}^2\\ =\left(5a^2+4b\right)\left(5a^2-4b\right)\end{array}$

Thus, the correct option is B.