Chapter 4.5, Problem 20WE

To determine

To simplify the expression

  $3x\left(5-2x\right)+6x\left(x-2\right)$

Answer to Problem 20WE

  $10x-12$

Explanation of Solution

Given:

  $3x\left(5-2x\right)+6x\left(x-2\right)$

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

  $3x\left(5-2x\right)+6x\left(x-2\right)$

First use distributive property to remove any grouping symbol

  $\begin{array}{c}3x\left(5-2x\right)+6x\left(x-2\right)=2x\cdot 5-3x\times 2x+6x\cdot x-6\cdot 2\\ =10x-6x^2+6x^2-12\end{array}$

Now, add/subtract like terms.

As,

  $\begin{array}{c}10x-6x^2+6x^2-12=10x+\left(-6+6\right)x^2-12\\ =10x+0x^2-12\\ =10x-12\end{array}$

Thus, simplified form of given expression is

  $3x\left(5-2x\right)+6x\left(x-2\right)=10x-12$