Expressions and Equations Part I

Variable

a symbol that represents (stands for) a number

Example: x or y

Coefficient

a number in front of a variable

Example: 3x, the 3 is the coefficient

Constant

a number with no variable attached

Example: 4, or in (w + 5), the 5 is a constant

Terms

variables, numbers, or the product of a number and variable(s) separated by addition or subtraction signs

Example:
One Term: x or 4y
Two Terms: 3z + 2
Three Terms: 8w - 7t + 9

Algebraic Expression

A mathematical phrase that can contain numbers, variables and operations(+,-,x,÷)

Examples: a + 1 or a - b or 3x

Base

a number or variable with an exponent on it

Like Terms

Like Terms have the same variable base and exponent
example: 3x and 6x

How to:
Combine Like Terms

add the coefficients & keep the variables the same (do not + or - exponents)
The sign in front of each term is part of the term

4y² + 7y² = 11y²
You can't add 3x + 6x²

Distributive Property
(with variables)

a(b+c) = a(b) + a(c)
Always distribute before combining like terms

Example:

6(2+4x) =

6(2) + 6(4x) =

12 + 24x

Monomial

One Term
Example: 3x

Binomial

Two terms or monomials, connected through addition or subtraction
Example: 3x - 6

Trinomial

Three terms or monomials, connected through addition or subtraction

Example: 3x² - 6x + 4

Polynomial

an expression that is a monomial, binomial, trinomial, or larger

Adding Polynomials

Just like combining like terms
Example:

(3x² + 2x + 9)

+

(4x² + 6x - 1)

= (7x² + 8x + 8)

Subtracting Polynomials

1 - Rewrite 1st polynomial

2 - Change subtraction to addition

3 - Change the signs of EVERY term in the 2nd polynomial

4 - Combine like terms

(3x + 2xy + 7) - (6x - 4xy + 3)

(3x + 2xy + 7) + (-6x + 4xy - 3)

= -3x + 6xy + 4

To Find:
Greatest Common Factor (GCF)

Method 1

1) Completely factor each number (list all the factors)
2) The largest number they have in common is the answer

To Find:
Greatest Common Factor (GCF)

Method 2

1) Divide the numbers by any common factor
2) Check to see if the quotients can be divided by another common factor

3) Continue to divide by common factors until the only common factor is 1

4) The GCF will be the product of all the divisors (the common factors you divided by)

Use GCF to Factor Linear Expressions

6x + 18

1) Find the GCF of the coefficient & the constant GCF of 6 & 18 is 6


2) Divide the original problem by the GCF to get the second factor


(6x+18) / 6

= x + 3


3) Write your answer as the product of the GCF & the Quotient 6(x + 3)

Using GCF to Factor Linear Expressions with Fractions

Use Rules for Using GCF to Factor Linear Expressions
***Differences:

1) change mixed numbers to improper fractions

2) need common denominators

3) find the GCF of the fractions (the gcf of the numerators over the common denominator)

LOOK BACK AT YOUR NOTES, THIS IS TOUGH