Chapter 4, Problem 13CT

To determine

To multiply the expression $2x\left(5-4x\right)$ .

Answer to Problem 13CT

  $10x-8x^2$

Explanation of Solution

Given information:

The expression, $2x\left(5-4x\right)$

Concept used:

• The distributive property of binomials (FOIL): $\left(a+b\right)\left(c+d\right)=a\cdot c+a\cdot d+b\cdot c+b\cdot d$
• Left distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$
• Product property of exponents: $x^n\cdot x^m=x^{n+m}$

Calculation:

In order to simplify the given expression $2x\left(5-4x\right)$ , use the distributive property to distribute the number inside the parenthesis and then simplify further by using the product property of exponents as shown below

  $\begin{array}{c}2x\left(5-4x\right)=2x\cdot 5+2x\cdot \left(-4x\right)\\ =10x-8x^2\end{array}$

Thus, the given expression simplifies to $10x-8x^2$ .