Question

In the following exercises, translate the phrases into algebraic expressions.

(a) eleven times the sum of $4x^2$ and 5x

(b) the sum of eleven times $4x^2$and 5x

Short answer

Part (a). The obtained expression is $4x^2+5x$.

Part (b). The obtained expression is $44x^2+5x$.

Step-by-step solution

Part (a). Step 1. Given Information

The given phrase is "eleven times the sum of$4x^2$ and 5x ."

Part (a). Step 2. Identify the operation for the phrase. 

The word "times" denoted "the operation of multiplication" and "sum" denotes "the operation of addition."

Part (a). Step 3. Write the algebraic expression.   

Since eleven is multiplied by the sum, use parenthesis to group the appropriate sum.

$4x^2+5x$

Part (b). Step 1. Given Information.

The given phrase is "the sum of eleven times$4x^2$and 5x.

Part (b). Step 2. Determine the numbers to be added.

• The word "of" and "and" shows that there are two numbers and the numbers are "eleven times $4x^2$that is $44x^2$" and "5x".
• Write the algebraic expression for the given phrase by adding both the mentioned numbers.

$44x^2+5x$