Chapter 7.2, Problem 42IP

To determine

To simplify the expression $2\left(x-y\right)-\left(x+y\right)$

Answer to Problem 42IP

  $x-3y$

Explanation of Solution

Given information:

The expression, $2\left(x-y\right)-\left(x+y\right)$

Concept used:

• The distributive property of binomials (FOIL): $\left(a+b\right)\left(c+d\right)=a\cdot c+a\cdot d+b\cdot c+b\cdot d$
• Left Distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$
• Exponent property: $x^n\cdot x^m=x^{n+m}$

Calculation:

In order to simplify the given expression, use the left distributive property and simplify the like terms as shown below

  $\begin{array}{c}2\left(x-y\right)-\left(x+y\right)\\ =2\cdot x+2\cdot \left(-y\right)-\left(x+y\right)\\ =2x-2y-x-y\\ =x-3y\end{array}$

Thus, the given expression simplifies to $x-3y$