# Distributive Property, Collecting Similar Terms, and Factoring by hcj

VIEWS: 0 PAGES: 8

• pg 1
```									Distributive Property, Collecting
Similar Terms, and Factoring

Use of Equivalent
Expressions to simplify
similar (like) terms
Equivalent Expressions

Equivalent Expressions are expressions which
always result in the same number when we
substitute values for the variables.
2(x+3) and 2x + 6 are equivalent expressions
Check: Let x = 4
2(4+3) = 2(4)+6
2(7) = 8+6
14 = 14
Distributive Property

Forms of the distributive property:
a(b + c) = ab + ac Note: You can distribute a
number from either side!
(b + c)a = ba + ca
Examples: 3(x + 5) = 3x + 15
7(x + 3 – y) = 7x + 21 – 7y
(r + s)x = rx + sx
Similar (Like) Terms

l   Similar or like terms are terms that have
exactly the same bases and exponents.
l       3x2       and    5x2 are similar terms
Coefficient      Exponent   Coefficient          Exponent
Base                            Base

7x and 16x2 are NOT similar terms
because the exponents are not exactly the
same.
Collecting Similar Terms

l   To collect like terms we use the distributive
property in reverse.

The rule for collecting like terms is to:
1) Copy the bases and exponents, and
2) Add or subtract the coefficients
Collecting Like Terms (More Examples)

42x + 6 + 4x + 2 = 42x + 4x + 6 + 2
= (42 + 4)x + (6 + 2)

Factoring (Greatest Common Factor)

l Factoring using the Greatest Common Factor is
the distributive property in reverse.
l Example: Factor 6x + 24
The GCF between 6 and 24 is 6, so