Chapter 5.10, Problem 60WE

To determine

To factor : the given expression

Answer to Problem 60WE

The result of factoring the given expression is $\boxed{\left(h-2k\right)\left(h+2k+4\right)}$

Explanation of Solution

Given information : $h^2-4k^2+4h-8k$

Concept Involved:

Rewrite the expression whenever required, then factor the expression as much as possible. Whenever we factor something, we divide each term by what we factor out to get the expression inside the parenthesis.

Formula used:

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

Calculation:

Rewrite the 2^nd term of the given expression

  $h^2-2^2{k}^2+4h-8k=h^2-{\left(2k\right)}^2+4h-8k$

Use the algebraic identity $a^2-b^2=\left(a+b\right)\left(a-b\right)$ to rewrite the first two terms of the equation$\left(h+2k\right)\left(h-2k\right)+4h-8k$

Factor 4 from last two terms of the expression

  $\left(h+2k\right)\left(h-2k\right)+4\left(h-2k\right)$

Factor the common binomial $\left(h-2k\right)$ from the whole expression

  $\left(h-2k\right)\left(h+2k+4\right)$

Conclusion:

Factoring $h^2-4k^2+4h-8k$ we get $\boxed{\left(h-2k\right)\left(h+2k+4\right)}$