Question

Simplify each expression.

$76.\left(5x-y\right)+\left(-8x+7y\right)$

Short answer

The simplified form of the expression is $-3x+6y$.

Step-by-step solution

Step-1 – Apply the concept of like terms

In an expression, the terms containing the same variable are like terms.

Step-2 – Example for the like terms

In the expression $4p-2q+p+3q$, the like terms are the terms which contain variable. So, the terms containing the variable p are $4p\text{and}p$ and the terms containing the variable q $-2q\text{and}3q$.

Step-3 – Simplify the expression

Consider the provided expression.

$\left(5x-y\right)+\left(-8x+7y\right)$

Open the brackets. Recall that negative sign when multiplied with positive results in negative sign.

$\left(5x-y\right)+\left(-8x+7y\right)=5x-y-8x+7y$

Group the like terms. Constant terms together, terms with variable x together and term with variable y together.

$\begin{array}{l}(5x-y)+(-8x+7y)=5x-y-8x+7y\\ =5x-8x-y+7y\\ =-3x+6y\end{array}$

Hence, the simplified form of the expression $\left(5x-y\right)+\left(-8x+7y\right)$ is $-3x+6y$.