Q. 5.57 - Intermediate Algebra

Question

Multiply :$$\begin{gathered} \left(a\right) (x^2+6)(x-8) \\ \left(b\right) (2ab+5)(4ab-4) \end{gathered}$$

Step-by-Step Solution

Answer

$$\begin{gathered} Open the brackets and Multiple the Binomials \\ \left(a\right) (x^2+6)(x-8) \\ x^3-8x^2+6x-48 \\ \left(b\right) (2ab+5)(4ab-4) \\ 8a^2{b}^2+12ab-20 \end{gathered}$$

Step 1

$$\begin{gathered} Given Information \\ \left(a\right) (x^2+6)(x-8) \\ \left(b\right) (2ab+5)(4ab-4) \end{gathered}$$

Step 2

The mnemonic FOILFOIL tells us exactly what terms to multiply, and in what order:

• First – multiply the first terms
• Outside – multiply the outside/outer terms
• Inside – multiply the inside/inner terms
• Last – multiply the last terms

Part(a) Step1. Multiply by FOIL method

$$\begin{gathered} \left(a\right) \\ 1.Multilpy first term x^3 \\ 2.Multiply outer term x^3-8x^2 \\ 3.Mulitply inner terms x^3-8x^2+6x \\ 4. Multiply last terms x^3-8x^2+6x-48 \\ 5. Combine like terms x^3-8x^2+6x-48 \end{gathered}$$

Part(b) Step1 Multiply by FOIL Method

$$\begin{gathered} \left(b\right) \\ 1. Multiply first term 8a^2{b}^2 \\ 2. Mulitply outer terms 8a^2{b}^2-8ab \\ 3. Multiply inner terms 8a^2{b}^2-8ab+20ab \\ 4. Multiply last terms 8a^2{b}^2-8ab+20ab-20 \\ 5. Combine like terms 8a^2{b}^2+12ab-20 \end{gathered}$$