What is the purpose of the distributive property?

1 Answer
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(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#