Chapter 8.3, Problem 6LC

To determine

To find: The best method to solve the expression $\left(3x+8\right)\left(x+1\right)$ among using a table, the distributive property, and FOIL method

Answer to Problem 6LC

Distributive Method is most efficient

Explanation of Solution

Given information:

  $\left(3x+8\right)\left(x+1\right)$

Calculation:

Using a table,

	$3x$	$8$
$x$	$3x^2$	$8x$
$1$	$3x$	$8$

To find the product $\left(3x+8\right)\left(x+1\right)$ , sum all the terms:

  $\begin{array}{l}\left(3x+8\right)\left(x+1\right)=3x^2+8x+3x+8\\ \left(3x+8\right)\left(x+1\right)=3x^2+11x+8\end{array}$

FOIL Method:

  $\begin{array}{l}\left(3x+8\right)\left(x+1\right)=3\left(x^2\right)+3x\left(1\right)+8\left(x\right)+8\left(1\right)\\ \left(3x+8\right)\left(x+1\right)=3x^2+3x+8x+8\\ \left(3x+8\right)\left(x+1\right)=3x^2+11x+8\end{array}$

Distributive Property:

  $\begin{array}{l}\left(3x+8\right)\left(x+1\right)=3x\left(x+1\right)+8\left(x+1\right)\\ \left(3x+8\right)\left(x+1\right)=3x^2+3x+8x+8\\ \left(3x+8\right)\left(x+1\right)=3x^2+11x+8\end{array}$

Distributive Method is most efficient