Expressions and the Distributive Property

Key Questions

  • 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!

  • 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'

  • 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

  • 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

Questions