Chapter 14, Problem 38SGR

To determine

To calculate: The value of $\left(x-3y\right)\left(2x-y\right)$ by multiplication model.

Answer to Problem 38SGR

The requiredmultiplication of the expression $\left(x-3y\right)\left(2x-y\right)$ is $2x^2-4xy+3y^2$ .

Explanation of Solution

Given Information:

The expression is $\left(x-3y\right)\left(2x-y\right)$ .

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 $\left(x-3y\right)\left(2x-y\right)$ .

Find the multiplication of the expression $\left(x-3y\right)\left(2x-y\right)$ .

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

  $\left(x-3y\right)\left(2x-y\right)=\left(x\right)\left(2x-y\right)+\left(-3y\right)\left(2x-y\right)$

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

  $\left(x\right)\left(2x-y\right)+\left(-3y\right)\left(2x-y\right)=\left(x\right)\left(2x\right)+\left(x\right)\left(-y\right)+\left(-3y\right)\left(2x\right)+\left(-3y\right)\times \left(-y\right)$

Use multiplication on the right hand side and simplify.

  $\begin{array}{c}\left(x\right)\left(2x-y\right)+\left(-3y\right)\left(2x-y\right)=\left(x\right)\left(2x\right)+\left(x\right)\left(-y\right)+\left(-3y\right)\left(2x\right)+\left(-3y\right)\times \left(-y\right)\\ =2x^2-xy-3xy+3y^2\\ =2x^2-4xy+3y^2\end{array}$

Hence, the required multiplication of the expression $\left(x-3y\right)\left(2x-y\right)$ is $2x^2-4xy+3y^2$ .