What is the purpose of the distributive property?

Feb 11, 2015

The distributive property allows you to distribute a coefficient in front of a set of paretheses by multiplying the coefficient times the two or more terms inside the parentheses, then adding the result. The basic form is $a \left(b + c\right) = a b + a c$.

If the coefficient and the contents of the parentheses are all numbers, such as $6 \left(3 + 8\right)$, then you can use the order of operations and add the contents of the parentheses, then multiply times the coefficient:

$6 \left(3 + 8\right) = 6 \left(11\right) = 66$

You can also use the distributive property:

6(3+8)=6·3+6·8=18+48=66

When you have unlike terms, you cannot use the order of operations and add the contents of the parentheses first. This is where the distributive property comes in.

Examples:

4(x+y)=4·x+4·y=4x+4y

5(7+3x)=5·7+5·3x=35+15x

a(x^2+b)=a·x^2+a·b=ax^2+ab

-(2+y)=-1·2+ -1·y=-2-y

4(a+b+c)=4·a+4·b+4·c=4a+4b+4c