Q54. - Algebra 2

Question

Simplify each expression

$4\left(14c-10d\right)-6\left(d+4c\right)$

Step-by-Step Solution

Answer

$4\left(14c-10d\right)-6\left(d+4c\right)$ is simplified to $2\left(16c-23d\right)$

Step 1 - 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	$a\left(b+c\right)=ab+ac\text{ and }\left(b+c\right)a=ba+ca$

Step 2 - 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

$\begin{array}{c}4\left(14c-10d\right)-6\left(d+4c\right)=56c-40d-6d-24c\\ =56c-40d-24c-6d\\ =56c-24c-40d-6d\\ =\left(56-24\right)c-\left(40+6\right)d\end{array}$

Step 3 - Use distributive property

Firstly simplify parentheses then take out common factor of both terms as shown below

 $\begin{array}{c}\left(56-24\right)c-\left(40+6\right)d=32c-46d\\ =2\left(16c-23d\right)\end{array}$