Chapter 8.3, Problem 22PPE

To determine

To simplify the given product $\left(k-6\right)\left(k+8\right)$ using the FOIL method.

Answer to Problem 22PPE

The product of given expression is $k^2+2k-48.$

Explanation of Solution

Given information:

Given expression $\left(k-6\right)\left(k+8\right)$

FOIL method is used to multiply two binomials. The letters in FOIL refer to two terms multiplied together in a certain order: First, Outer, Inner and Last.

i.e. Multiply each term in the first binomial $\left(k-6\right)$ with each term in the second binomial $\left(k+8\right).$ Thus, multiply the first term of each binomial together: $k\times \left(k\right)=k^2$

Multiply the outer terms together: $k\times \left(8\right)=8k$

Multiply the inner terms together: $-6\times \left(k\right)=-6k$

Multiply the last term of each binomial together: $-6\times \left(8\right)=-48$

  $\begin{array}{l}\Rightarrow \left(k-6\right)\left(k+8\right)=k^2+8k-6k-48\\ \therefore \left(k-6\right)\left(k+8\right)=k^2+2k-48.\end{array}$

Hence, the product of given expression is $k^2+2k-48.$