Q5.55 - Intermediate Algebra

Question

Multiply :$$\begin{gathered} \left(a\right) (x-7)(x+5) \\ \left(b\right) (3x+7)(5x-2) \end{gathered}$$

Step-by-Step Solution

Answer

Multiply the binomials ,we get

$$\begin{gathered} \left(a\right).(x-7)(x+5)= x^2-2x-35 \\ \left(b\right).(3x+7)(5x-2)=15x^2-29x-14 \end{gathered}$$

Step 1. Given information

$$\begin{gathered} \left(a\right) (x-7)(x+5) \\ \left(b\right) (3x+7)(5x-2) \end{gathered}$$

Step 2. FOIL method

$$\begin{gathered} The mnemonic F O I L tells us exactly what terms to multiply, and in what order: \\ First – multiply the first terms \\ Outside – multiply the outside/outer terms \\ Inside – multiply the inside/inner terms \\ Last – multiply the last terms \end{gathered}$$

Step 3 Part (a) Step 1. Multiply the binomials

    $$\begin{gathered} \left(a\right) \\ 1.Multiply first term x^2 \\ 2. Multiply outer term x^2+5x \\ 3. Mulitply inner term x^2+5x-7x \\ 4.Multiply in last term x^2+5x-7x-35 \\ 5. Combine like terms x^2-2x-35 \end{gathered}$$

Step 4 Part (b) Step 1.Multiply the binomials

$$\begin{gathered} \left(b\right) \\ 1.Mulitply first term 15x^2 \\ 2.Multiply outer term 15x^2-6x \\ 3.Multiply inner term 15x^2-6x+35x \\ 4.Multiply last term 15x^2-6x+35x-14 \\ 5. Combine like term 15x^2+29x-14 \end{gathered}$$