Question

Simplify each expression

$2\left(10m-7a\right)+3\left(8a-3m\right)$

Short answer

$2\left(10m-7a\right)+3\left(8a-3m\right)$ is simplified to $11m+10a$

Step-by-step solution

- Write properties of real numbers 

Properties of real numbers are written in following table:

For any real numbers a, b, and c:
Property	Addition	Multiplication
Commutative	a+b=b+a	$a·b=b·a$
Associative	$\left(a+b\right)+c=a+\left(b+c\right)$	$\left(a·b\right)·c=a·\left(b·c\right)$
Identity	a+0=a=0+a	$a·1=a=1·a$
Inverse	$a+\left(-a\right)=0=\left(-a\right)+a$	If $a\ne 0$, then $a·\frac{1}{a}=1=\frac{1}{a}·a$
Distributive	$a\left(b+c\right)=ab+ac\text{and}\left(b+c\right)a=ba+ca$

- Simplify by grouping same variables

To simplify given equation, first use distributive property then commutative property of addition then distributive property to group coefficients of same variable as shown below

$\begin{array}{c}2\left(10m-7a\right)+3\left(8a-3m\right)=20m-14a+24a-9m\\ =20m-14a-9m+24a\\ =20m-9m-14a+24a\\ =\left(20-9\right)m+\left(-14+24\right)a\end{array}$

- Simplify further

To simplify, evaluate parentheses as shown below

$\left(20-9\right)m+\left(-14+24\right)a=11m+10a$