Chapter 4.5, Problem 22WE

To determine

To simplify the expression

  $4y\left(2y^2-3y\right)-3y^2\left(y-4\right)$

Answer to Problem 22WE

  $5y^3$

Explanation of Solution

Given:

  $4y\left(2y^2-3y\right)-3y^2\left(y-4\right)$

Concept Used:

• To simplify an expression first use distributive property to remove any grouping symbol, and then add/subtract like terms.
• Distributive property: $a\left(b\pm c\right)=ab\pm ac$
• $a^m{a}^n=a^{m+n}$
• If an expression contains more than one operations between its terms and brackets, first solve the terms inside brackets and then apply division followed by multiplication, addition and subtraction.

Calculation:

To simplify the expression

  $4y\left(2y^2-3y\right)-3y^2\left(y-4\right)$

First use distributive property to remove any grouping symbol

  $\begin{array}{c}4y\left(2y^2-3y\right)-3y^2\left(y-4\right)=4y\cdot 2y^2-4y\cdot 3y-3y^2\cdot y+3y^2\cdot 4\\ =8y^3-12y^2-3y^3+12y^2\end{array}$

Now, add/subtract like terms.

As,

  $\begin{array}{c}8y^3-12y^2-3y^3+12y^2=\left(8-3\right)y^3+\left(-12+12\right)y^2\\ =5y^3+0y^2\\ =5y^3\end{array}$

Thus, simplified form of given expression is

  $4y\left(2y^2-3y\right)-3y^2\left(y-4\right)=5y^3$