Question

Simplify each expression.

$\text{5}\left(4x+2y-x+2\right)$

Short answer

The simplified form of the expression is $15x+10y+10$.

Step-by-step solution

Step-1 – Apply the concept of multiplication and like terms

In an expression, when a constant term is multiplied with term containing variables, then multiply the constant part of term and variable remain as it is.

In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

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

Step-2 – Example for the multiplication

In the expression, $6\left(4p\right)$, the constant term 6 is to multiplied with $4p$, so multiplied 4 and 6 and p remains as it is. The result obtained is $6\left(4p\right)=24p$.

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 are $-2q\text{and}3q$.

Step-3 – Simplify the expression

Consider the provided expression.

$5\left(4x+2y-x+2\right)$

Multiply 5 with the terms inside the bracket. Recall that negative sign when multiplied with positive results in negative sign

$\begin{array}{l}5(4x+2y-x+2)=5\left(4x\right)+5\left(2y\right)+5(-x)+5\left(2\right)\\ =20x+10y-5x+10\end{array}$

Group the like terms. Constant terms together and terms with variable x together.

$\begin{array}{l}5(4x+2y-x+2)=20x+10y-5x+10\\ =20x-5x+10y+10\\ =15x+10y+10\end{array}$

This cannot be further simplified.

Hence, the simplified form of the expression $5\left(4x+2y-x+2\right)$ is $15x+10y+10$.