# Which property justifies each step? (6+2)a + 8b = 8a + 8b.

## Question:

Which property justifies each step? {eq}(6+2)a + 8b = 8a + 8b. {/eq}

## Distributive Property

An algebraic expression is an expression which consists of constants, variables and algebraic operations like addition, subtraction, product and division.

If there are two linear algebraic expressions as

{eq}\displaystyle f(x)\ =\ ax\ +\ b\\ \displaystyle g(x)\ =\ cx\ +\ d {/eq}

then according to the distributive property, their product can be written as

{eq}\displaystyle f(x)\ \times\ g(x)\ =\ (ax\ +\ b)\ \times\ ( cx\ +\ d)\ =\ ax\ \times\ (cx\ +\ d)\ +\ b\ \times\ (cx\ +\ d) {/eq}

## Commutative Property

According to the Commutative Property, if any operation is operated between two numbers, let's say a and b then the result will be same if it is applied between b and a.

Mathematically, according to this property,

{eq}\displaystyle a\ f\ b\ =\ b\ f\ a {/eq}

where:

• f is the operation like addition or multiplication

## Associative Property

We can multiply or add three or more than three numbers without considering the positions of the numbers.

For example, if we have three numbers as, a, b and c then using this property we can write

{eq}\displaystyle a\ +\ (b\ +\ c)\ =\ (a\ +\ b)\ +\ c\ =\ (a\ +\ c)\ +\ b\\ \displaystyle a\ \times\ (b\ \times\ c)\ =\ (a\ \times\ b)\ \times\ c\ =\ (a\ \times\ c)\ \times\ b {/eq}

Here we have,

{eq}(6+2)a + 8b = 8a + 8b. {/eq}

The first term shows the distribution property.