Question

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

(a) The sum of $4a{b}^2$and $3a^{2}b$

(b) the product of $4y^2$ and 5x

(c) Fifteen more than m

(d) 9xless than$121x^2$

Short answer

Part (a). The obtained expression is $4a{b}^2+3a^{2}b$.

Part (b). The obtained expression is$20x{y}^2$.

Part (c). The obtained expression is$m+15$.

Part (d). The obtained expression is$x\left(121x-9\right)$.

Step-by-step solution

Part (a). Step 1. Given Information

The given phrase is "the sum of$4a{b}^2$and$3a^{2}b$."

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

The word "sum" denoted "the operation of addition."

Part (a). Step 3. Determine the numbers to be added.

• The word "of" and "and" shows that there are two numbers and the numbers are $4a{b}^2$and$3a^{2}b$.
• The given phrase will be "$4a{b}^2$added to $3a^{2}b$."

$4a{b}^2+3a^{2}b$

Part (b). Step 1. Given Information.

The given phrase is "the product of "$4y^2$and 5x."

Part (b). Step 2. Write the algebraic expression for the given phrase.  

• Refer to the process mentioned in the previous part.
• The keyword "product" denotes "the multiplication operation."
• After a look at the word "of" and "and", the phrase will be "multiply $4y^2$ and 5x."
• Simplify.

$4y^2\left(5x\right)=20x{y}^2$

Part (c). Step 1. Given Information.  

The given phrase is "fifteen more thanm."

Part (c). Step 2. Write the algebraic expression for the given phrase.   

• Refer to the process mentioned in the part (a).
• The keyword "more than" denotes "the addition operation" and it means "added to."
• The given phrase will be "fifteen added tom.

$m+15$

Part (d). Step 1. Given Information.  

The given phrase is "9xless than$121x^2$."

Part (d). Step 2. Write the algebraic expression for the given phrase.

• Refer to the process mentioned in part (a).
• The keyword "less than" denotes "the subtraction operation" and it means "subtracted from."
• The given phrase will be "9xsubtracted from$121x^2$."
• Simplify.

$121x^2-9x=x\left(121x-9\right)$