Expressions and the Distributive Property

Key Questions

How do you use the distributive property with variables?
Answer:

See examples below
Explanation:
Whatever is outside of the parenthesis, we must multiply it by all terms on the inside.

Example: #11(3x+9y)#

In this case, we would multiply the #11# by both of the terms in the parenthesis to get

#33x+99y#

What if we have two sets of parenthesis?

#(2x+8)(3x+11)#

We multiply every term in the first parenthesis by everyone in the second. We are essentially doing the distributive property twice.

This method is sometimes called FOIL, standing for Firsts, Outsides, Insides, Lasts. This is the order we multiply in. Going back to our example

#(2x+8)(3x+11)#

We multiply the first terms: #2x*3x=color(lime)(6x^2)#

Outside terms: #2x*11=color(lime)(22x)#

Inside terms: #8*3x=color(lime)(24x)#

Last terms: #8*11=color(lime)(88)#

Now we have

#6x^2+22x+24x+88# which can be simplified to

#6x^2+46x+88#

Hope this helps!
Jacobi J. · 1 · May 17 2018
Why is the distributive property important?

The distributive property says that #a(b+c)=a*b+a*c#

Without this you wouldn't be able the expand expressions like:

#(x+1)(2x-4)# into

#x(2x-4)+1(2x-4)#, then

#x*2x+x*(-4)+1*2x+1*(-4)# and then

#2x^2-4x+2x-4=2x^2-2x-4#

In other words, you would not be able to 'clear the brackets'

MeneerNask · 2 · Jan 9 2015
How do you use the distributive property to find a product mentally?

Answer:

See examples below

Explanation:

Distributive property is #a(b+c)=ab+ac# and also #(a+b)(c+d)=ac+ad+bc+bd#

Imagine you want calculate #7·25#

In this case you can say #7(20+5)=140+35=175#

Another one: #23·42=(20+3)·(40+2)=20·40+20·2+3·40+2·3=800+40+120+6=966#

F. Javier B. · 1 · May 2 2018
What is the Distributive Property?

Answer:

see below

Explanation:

Let's think about matrices. #AB ne BA#

Left distribution

#A ( B + C) = AB + AC#

#2 ( B + C) = 2B + 2C#

Right distribution

#(A + B) C = AC + BC#

#(A + B)* 2 = A*2 + B*2#

Vinícius Ferraz · 1 · May 23 2018