Chapter 14, Problem 35SGR

To determine

To calculate: The value of $\left(2y-1\right)\left(y+9\right)$ by multiplication model.

Answer to Problem 35SGR

The requiredmultiplication of the expression $\left(2y-1\right)\left(y+9\right)$ is $2y^2+17y-9$ .

Explanation of Solution

Given Information:

The expression is $\left(2y-1\right)\left(y+9\right)$ .

Formula Used:

The distributive formula is:

  $\left(a+b\right)\left(c+d\right)=a\left(c+d\right)+b\left(c+d\right)$

Calculation:

The given expression is $\left(2y-1\right)\left(y+9\right)$ .

Find the multiplication of the expression $\left(2y-1\right)\left(y+9\right)$ .

Use the distributive formula $\left(a+b\right)\left(c+d\right)=a\left(c+d\right)+b\left(c+d\right)$

  $\left(2y-1\right)\left(y+9\right)=2y\left(y+9\right)+\left(-1\right)\left(y+9\right)$

Use again distributiveformula $\left(a+b\right)\left(c+d\right)=a\left(c+d\right)+b\left(c+d\right)$

  $2y\left(y+9\right)+\left(-1\right)\left(y+9\right)=\left(2y\right)\left(y\right)+9\left(2y\right)+\left(-1\right)\left(y\right)+\left(-1\right)\times 9$

Use multiplication on the right hand side and simplify.

  $\begin{array}{c}2y\left(y+9\right)+\left(-1\right)\left(y+9\right)=\left(2y\right)\left(y\right)+9\left(2y\right)+\left(-1\right)\left(y\right)+\left(-1\right)\times 9\\ =2y^2+18y-y-9\\ =2y^2+17y-9\end{array}$

Hence, the required multiplication of the expression $\left(2y-1\right)\left(y+9\right)$ is $2y^2+17y-9$ .