Q79. - Algebra 2

Question

Simplify each expression. 

$79.\text{ 3}\left(x+4y\right)-2\left(x+4y\right)$

Step-by-Step Solution

Answer

The simplified form of the expression is $\backslash [x+4y\backslash ].$

Step-1 – Apply the concept of Distributive property and like terms

The distributive property is stated below.

$a\left(b+c\right)=ab+ac$

Where a, b and c are real numbers.

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

Step-2 – Example for the Distributive property and like terms

$2\left(p+q\right)=2p+2q$

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

Step-3 – Simplify the expression

$\begin{array}{l}3(x+4y)-2(x+4y)=3\left(x\right)+3\left(4y\right)-2\left(x\right)-2\left(4y\right)\\ =3x+12y-2x-8y\\ =3x-2x+12y-8y\\ =x+4y\end{array}$

This cannot be further simplified.

Hence, the simplified form of the expression $3\left(x+4y\right)-2\left(x+4y\right)$ is $x+4y$.

Consider the provided expression.

$3\left(x+4y\right)-2\left(x+4y\right)$

Apply the distributive property.

$3\left(x+4y\right)-2\left(x+4y\right)=3\left(x\right)+3\left(4y\right)-2\left(x\right)-2\left(4y\right)$

Multiply 3 and 2 with the terms inside the bracket. Recall that negative sign when multiplied with positive results in negative sign.

$\begin{array}{l}3(x+4y)-2(x+4y)=3\left(x\right)+3\left(4y\right)-2\left(x\right)-2\left(4y\right)\\ =3x+12y-2x-8y\end{array}$

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