Chapter 8.3, Problem 25PPE

To determine

To simplify the given product $\left(9z+4\right)\left(5z-3\right)$ using the FOIL method.

Answer to Problem 25PPE

The product of given expression is $45z^2-7z-12.$

Explanation of Solution

Given information:

Given expression $\left(9z+4\right)\left(5z-3\right)$

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 $\left(9z+4\right)$ with each term in the second binomia $\left(5z-3\right).$

Thus, multiply the first term of each binomial together: $\left(9z\right)\times \left(5z\right)=45z^2$

Multiply the outer terms together: $\left(9z\right)\times \left(-3\right)=-27z$

Multiply the inner terms together: $4\times \left(5z\right)=20z$

Multiply the last term of each binomial together: $4\times \left(-3\right)=-12$

  $\begin{array}{l}\Rightarrow \left(9z+4\right)\left(5z-3\right)=45z^2-27z+20z-12\\ \therefore \left(9z+4\right)\left(5z-3\right)=45z^2-7z-12.\end{array}$

Hence, the product of given expression is $45z^2-7z-12.$