Question

What is the purpose of the distributive property?

Answer 1

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(b + c) = ab + ac`.

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

`6(3+8)=6(11)=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`