Chapter B.3, Problem 1P

To determine

To multiply: The monomial $3y$ by the polynomial $7y^2+5$.

Answer to Problem 1P

The expression $3y\left(7y^2+5\right)$ can be simplified as $\underset{\_}{21y^3+15y}$.

Explanation of Solution

Property used:

Distributive Property:

Let a, b and c be real numbers then, $a\left(b+c\right)=a\cdot b+a\cdot c$.

Calculation:

Use distributive property and simplify $3y\left(7y^2+5\right)$ as follows.

$\begin{array}{c}3y\left(7y^2+5\right)=3y\left(7y^2\right)+3y\left(5\right)\\ =21y^{1+2}+15y\\ =21y^3+15y\end{array}$

Therefore, the expression $3y\left(7y^2+5\right)$ can be simplified as $\underset{\_}{21y^3+15y}$.