Q5.62 - Intermediate Algebra

Question

Multiply $(x+4)(2x^2-3x+5)$ using (a) the distributive property (b) Vertical method.

Step-by-Step Solution

Answer

$$\begin{gathered} Multiply the given binomials, we get \\ (x+4)(2x^2-3x+5)=2x^3+5x^2-7x+20 \end{gathered}$$

Step1

$$\begin{gathered} Given Information: \\ Multiply (x+4)(2x^2-3x+5) by distributive property and vertical method. \end{gathered}$$

Step 2

The Distributive Property is an algebraic property that is used to multiply a single value and two or more values within a set of parenthesis. 

Vertical addition is a method of adding where the numbers are lined up in columns according to their places value. 

Part(a) Step 1. Multiply the binomials by distributive property.

$$\begin{gathered} \left(a\right) \\ Distribute x\times 2x^2-3x\times x+5\times x+4\times 2x^2-4\times 3x+4\times 5 \\ Distribute again 2x^3-3x^2+5x+8x^2-12x+20 \\ Add like terms 2x^3+5x^2-7x+20 \end{gathered}$$

Part(b) Step 1. Multiply the binomials by vertical method.

$$\begin{gathered} \left(b\right) \\ 2x^2-3x+5 \\ \times (x+4) \\ Multiple 2x^2-3x+5 by 4 8x^2-12x+20 partial product \\ Multiple 2x^2-3x+5 by x 2x^3-3x^2+5x partial product \\ Add like terms 2x^3+5x^2-7x+20 \end{gathered}$$