Q5.58 - Intermediate Algebra

Question

Multiply :$$\begin{gathered} \left(a\right) (y^2+7)(y-9) \\ \left(b\right) (2xy+3)(4xy-5) \end{gathered}$$

Step-by-Step Solution

Answer

$$\begin{gathered} Multiply the given binomials,we get \\ \left(a\right) (y^2+7)(y-9) \\ y^3-9y^2+7y-63 \\ \left(b\right) (2xy+3)(4xy-5) \\ 8x^2{y}^2+2xy-15 \end{gathered}$$

Step 1

$$\begin{gathered} Given Information \\ \left(a\right) (y^2+7)(y-9) \\ \left(b\right) (2xy+3)(4xy-5) \end{gathered}$$

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) Step 1.Multiply binomials by FOIL method

$$\begin{gathered} \left(a\right) \\ 1.Multipy first terms y^3 \\ 2. Mulitply outer terms y^3-9y^2 \\ 3. Multiply inner terms y^3-9y^2+7y \\ 4. Multiply last terms y^3-9y^2+7y-63 \\ 5. Combine last terms y^3-9y^2+7y-63 \end{gathered}$$

Part(b).Step 1.Multiply binomials by FOIL method

$$\begin{gathered} \left(b\right) \\ 1. Multiply first terms 8x^2{y}^2 \\ 2. Multiply outer terms 8x^2{y}^2-10xy \\ 3. Multiply inner terms 8x^2{y}^2-10xy+12xy \\ 4. Mulitply last terms 8x^2{y}^2-10xy+12xy-15 \\ 5. Combine last terms 8x^2{y}^2+2xy-15 \end{gathered}$$