Chapter 8.3, Problem 42PPS

To determine

To find: The product $\left(4y+3z\right){\left(4y-3z\right)}^2$

Answer to Problem 42PPS

  $64y^3-48y^{2}z-36y{z}^2+27z^3$

Explanation of Solution

Given:

  $\left(4y+3z\right){\left(4y-3z\right)}^2$

Calculation:

The given expression is $\left(4y+3z\right){\left(4y-3z\right)}^2$

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

  $\begin{array}{l}\left(4y+3z\right){\left(4y-3z\right)}^2\\ =\left(4y+3z\right)\left(16y^2-24yz+9z^2\right)\end{array}$

Now, multiply using the distributive property

  $\begin{array}{l}4y\cdot 16y^2+4y\cdot \left(-24yz\right)+4y\cdot 9z^2+3z\cdot 16y^2+3z\cdot \left(-24yz\right)+3z\cdot 9z^2\\ =64y^3-96y^{2}z+36y{z}^2+48y^{2}z-72y{z}^2+27z^3\\ =64y^3-48y^{2}z-36y{z}^2+27z^3\end{array}$