Question

Translate the English phrase into an algebraic expression:

$$\begin{gathered} \left(\text{a}\right)\text{thesumof}4a{b}^2\text{and}7a^3{b}^2 \\ \left(\text{b}\right)\text{theproductof}6y^2\text{and}3y \\ \left(\text{c}\right)\text{twelvemorethan}5x \\ \left(\text{d}\right)5y\text{lessthan}8y^2 \end{gathered}$$

Short answer

The algebraic expressions are

$$\begin{gathered} \left(\text{a}\right)4a{b}^2+7a^3{b}^2 \\ \left(\text{b}\right)\left(6y^2\right)\left(3y\right) \\ \left(\text{c}\right)5x+12 \\ \left(\text{d}\right)8y^2-5y \end{gathered}$$

Step-by-step solution

Step 1. Given information

The given phrases are

$$" width="9" height="19" role="math">athesumof4ab2and7a3b2btheproductof6y2and3yctwelvemorethan5xd5ylessthan8y2

Part a.Step 1. Translate into an algebraic expression

$$\begin{gathered} \left(\text{a}\right)\text{thesumof}4a{b}^2\text{and}7a^3{b}^2 \\ \Rightarrow 4a{b}^2+7a^3{b}^2 \end{gathered}$$

Part b. Step 1.Translate into an algebraic expression

$$\begin{gathered} \left(\text{b}\right)\text{theproductof}6y^2\text{and}3y \\ \Rightarrow \left(6y^2\right)\left(3y\right) \end{gathered}$$

Part c. Step 1.Translate into an algebraic expression

$$\begin{gathered} \left(\text{c}\right)\text{twelvemorethan}5x \\ \Rightarrow 5x+12 \end{gathered}$$

Part d. Step 1.Translate into an algebraic expression

$$\begin{gathered} \left(\text{d}\right)5y\text{lessthan}8y^2 \\ \Rightarrow 8y^2-5y \end{gathered}$$