Chapter 8.3, Problem 26PPE

To determine

To simplify the given product $\left(3h+2\right)\left(6h-5\right)$ using the FOIL method.

Answer to Problem 26PPE

The product of given expression is $18h^2-3h-10.$

Explanation of Solution

Given information:

Given expression $\left(3h+2\right)\left(6h-5\right)$

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 $\left(3h+2\right)$ with each term in the second binomia $\left(6h-5\right).$

Thus, multiply the first term of each binomial together: $\left(3h\right)\times \left(6h\right)=18h^2$

Multiply the outer terms together: $\left(3h\right)\times \left(-5\right)=-15h$

Multiply the inner terms together: $2\times \left(6h\right)=12h$

Multiply the last term of each binomial together: $2\times \left(-5\right)=-10$

  $\begin{array}{l}\Rightarrow \left(3h+2\right)\left(6h-5\right)=18h^2-15h+12h-10\\ \therefore \left(3h+2\right)\left(6h-5\right)=18h^2-3h-10.\end{array}$

Hence, the product of given expression is $18h^2-3h-10.$