Chapter 8, Problem 62CR

To determine

The solution of the given expression.

Answer to Problem 62CR

The factor of expression $9z^2-16$ is $\left(3z-4\right)\left(3z+4\right)$

Explanation of Solution

Given information:

The expression $9z^2-16$

Concept and Formula Used:

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

Calculation:

The given expression is $9z^2-16$

The expression can be written as

  $9z^2-16={\left(3z\right)}^2-{\left(4\right)}^2$

Using the property ${\left(a-b\right)}^2=a^2-2ab+b^2$

Therefore

  $9z^2-16=\left(3z-4\right)\left(3z+4\right)$

Conclusion:

The factor of expression $9z^2-16$ is $\left(3z-4\right)\left(3z+4\right)$