Download 2x x2

Distributive Property Notes
Words
To multiply a sum by a number, multiply each addend by the
number outside the parenthesis.
Example
Numbers
Algebra
2(7 + 4) = (2 x 7) + (2 x 4)
a(b + c) = (a x b) + (a x c)

When using the distributive property, draw arrows from the value
outside the parentheses to each value inside.

The arrows show what will be multiplied.

You are done solving when all parentheses are gone and all like terms
are combined.
You will often see a letter inside the parentheses. This is called a variable,
and is used to represent an unknown quantity.
2(x + 3)
variable
When you see a number in front of a variable with no spaces or symbols in
between, this means the variable is being multiplied by the number in front
of it.
 This number is called the coefficient and should NEVER be
written after the variable!
Yes!
2x
x2
NO!
Generate an equivalent expression using the distributive property
(simplify the expression).

1. 8(4 + x)
Step 1: Draw an arrow
from the number outside
the parentheses to each
number or term inside
the parentheses.

2. (x + 9)5
Factoring the Expression
When an expression is written as a product of its factors
o It’s basically the opposite of the distributive property ;)
Factor the following expressions.
5.
3x + 15
Ex: 3(5 + x)
Step 2: Rewrite the
expression as the sum of
two multiplication
problems:
(3 5) + (3 x)
Step 2: Write this number
(factor) outside a set of
empty parentheses.
6.
16 + 4x
Step 3: Solve or simplify
the expressions inside
the parentheses.
3. 7(x + y)
Step 3: Divide the first
term by that number and
write the quotient as the
first term inside the
parentheses.
Step 4: Write an addition
sign “+” after the first
term inside the
parentheses.
Step 4: Combine like
terms.
7.
4. 2(3x + 4y)
Step 1: Find the largest
number (factor) that
divides evenly into both
terms.
7x + 42y
Step 5: Divide the second
term by that same
number and write the
quotient as the second
term inside the
parentheses.
**QUESTIONS**