Chapter 8.5, Problem 27PPS

0

To determine

The factorization of the polynomial.

Answer to Problem 27PPS

  $6k^2\left(h-3k\right)\left(h+3k\right)$

Explanation of Solution

Given:

The given polynomial is:

  $6k^2{h}^2-54k^4$

Calculation:

It is known that,

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

The given polynomial can be written as:

  $\begin{array}{l}=6k^2{h}^2-54k^4\\ =6k^2\left(h^2-9k^2\right)\\ =6k^2\left({\left(h\right)}^2-{\left(3k\right)}^2\right)\\ =6k^2\left(h-3k\right)\left(h+3k\right)\end{array}$