Chapter SH, Problem 5.3EP

To determine

Find the simplified form of the given expression.

Answer to Problem 5.3EP

The simplified form of the expression is $6c^{2}d+8d^2+4dc-8c{d}^2$ .

Explanation of Solution

Given:

The given expression is $2cd\left(3c-4d\right)+4d\left(c+2d\right)$ .

Calculation:

  $2cd\left(3c-4d\right)+4d\left(c+2d\right)$

Remove parentheses, use distributive property.

  $=2cd\left(3c\right)+2cd\left(-4d\right)+4d\left(c\right)+4d\left(2d\right)$

Multiply the monomials.

  $\begin{array}{l}=6c^{2}d-8c{d}^2+4dc+8d^2\\ =6c^{2}d+8d^2+4dc-8c{d}^2\end{array}$

Hence the simplified form of the expression is $6c^{2}d+8d^2+4dc-8c{d}^2$ .