Chapter 4.7, Problem 5MRE

To determine

To simplify the expression $4x\left(x^2-3x+2\right)$ .

Answer to Problem 5MRE

  $4x^3-12x^2+8x$

Explanation of Solution

Given information:

The expression, $4x\left(x^2-3x+2\right)$

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: $a\left(b+c\right)=a\cdot b+a\cdot c$
• Exponent property: $x^n\cdot x^m=x^{n+m}$

Calculation:

In order to simplify the given expression $4x\left(x^2-3x+2\right)$ , first use the distributive property to expand the parenthesis and then simplify further by using the exponent property as shown below

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

Thus, the given expression simplifies to $4x^3-12x^2+8x$ .