Chapter 8.3, Problem 3P

a.

To determine

To find:The simpler form of the product $(3x-4)(x+2)$ using FOIL method.

Answer to Problem 3P

  $3x^2+2x-8$

Explanation of Solution

Given information:The expression $(3x-4)(x+2)$

Calculation:

  $\begin{array}{l}(3x-4)(x+2)\\ =(3x)(x)+(3x)(2)+(-4)(x)+(-4)(2)\\ =3x^2+6x-4x-8\\ =3x^2+2x-8\end{array}$

Thus, $(3x-4)(x+2)=3x^2+2x-8$

b.

To determine

To find:The simpler form of the product $(n-6)(4n-7)$ using FOIL method.

Answer to Problem 3P

  $4n^2-31n+42$

Explanation of Solution

Given information:The expression $(n-6)(4n-7)$

Calculation:

  $\begin{array}{l}(n-6)(4n-7)\\ =(n)(4n)+(n)(-7)+(-6)(4n)+(-6)(-7)\\ =4n^2-7n-24n+42\\ =4n^2-31n+42\end{array}$

Thus, $(n-6)(4n-7)=4n^2-31n+42$

c.

To determine

To find: The simpler form of the product $(2p^2+3)(2p-5)$ using FOIL method.

Answer to Problem 3P

  $4p^3-10p^2+6p-15$

Explanation of Solution

Given information:The expression $(2p^2+3)(2p-5)$

Calculation:

  $\begin{array}{l}(2p^2+3)(2p-5)\\ =(2p^2)(2p)+(2p^2)(-5)+(3)(2p)+(3)(-5)\\ =4p^3-10p^2+6p-15\end{array}$

Thus, $(2p^2+3)(2p-5)=4p^3-10p^2+6p-15$