Q5.56 - Intermediate Algebra

Question

Multiple :$$\begin{gathered} \left(a\right) (b-3)(b+6) \\ \left(b\right) (4y+5)(4y-10) \end{gathered}$$

Step-by-Step Solution

Answer

$$\begin{gathered} \left(a\right) (b-3)(b+6) \\ b\times b+6b-3b-18 \\ b^2+3b-18 \\ \left(b\right) (4y+5)(4y-10) \\ 4y\times 4y-10\times 4y+20y-50 \\ 16y^2-40y+20y-50 \\ 16y^2-20y-50 \end{gathered}$$

Step 1

$$\begin{gathered} Given information \\ \left(a\right) (b-3)(b+6) \\ \left(b\right) (4y+5)(4y-10) \end{gathered}$$

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

Step 3

$$\begin{gathered} Part\left(a\right).Step1 Multiple by FOIL method \\ \left(a\right) \\ 1.Multiply first term b^2 \\ 2. Multiply outer term b^2+6b \\ 3. Multiply inner term b^2+6b-3b \\ 4. Multilpy last term b^2+6b-3b-18 \\ 5. Combine like terms b^2+3b-18 \end{gathered}$$

Step 4

$$\begin{gathered} Part\left(b\right).Step1 Multiply by FOIL method \\ \left(b\right) \\ 1. Multiply first term 16y^2 \\ 2. Mulitply outer term 16y^2-40y \\ 3. Mulitply inner term 16y^2-40y+20y \\ 4. Multiply last term 16y^2-40y+20y-50 \\ 5. Combine like term 16y^2-20y-50 \end{gathered}$$