Chapter 4.5, Problem 21WE

To determine

To simplify the expression

  $6r^2\left(2r-1\right)-3r\left(4r^2-5r\right)$

Answer to Problem 21WE

  $9r^2$

Explanation of Solution

Given:

  $6r^2\left(2r-1\right)-3r\left(4r^2-5r\right)$

Concept Used:

• To simplify an expression first use distributive property to remove any grouping symbol, and then add/subtract like terms.
• Distributive property: $a\left(b\pm c\right)=ab\pm ac$
• 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

  $6r^2\left(2r-1\right)-3r\left(4r^2-5r\right)$

First use distributive property to remove any grouping symbol

  $\begin{array}{c}6r^2\left(2r-1\right)-3r\left(4r^2-5r\right)=6r^2\cdot 2r-6r^2-3r\cdot 4r^2-3r\cdot \left(-5r\right)\\ =12r^3-6r^2-12r^3+15r^2\end{array}$

Now, add/subtract like terms.

As,

  $\begin{array}{c}12r^3-6r^2-12r^3+15r^2=\left(12-12\right)r^3+\left(-6+15\right)r^2\\ =0r^3+9r^2\\ =9r^2\end{array}$

Thus, simplified form of given expression is

  $6r^2\left(2r-1\right)-3r\left(4r^2-5r\right)=9r^2$