Algebra Formulas Cheat Sheet page 2

Expression-Evaluating Expressions

Replace the variable with parentheses
Inside the parentheses place the value
Simplify and solve.

Step 1: 5(x) + 6 for x = 2
Step 2: 5(2) + 6
Step 3: 10 +6 =16

Expression-Writing Expressions

Look for key words of algebraic expressions.
Combine these written expressions with variables for unknown values into an algebraic expression.

Six less than twice the value: 2x-6
Five less than a number: x-5

Find slope from two points

Make a function table using the x and y values of two points

Subtract y₁ – y₂ equals Rise
Subtract x₁ –x₂ equals Run
Write as: Rise/Run

Function

f(x) = x^2

Greatest common factor

The greatest number that is the largest factor of two or more given numbers

GCF of 6 and 3 is 3 GCF of 6,12,36 is 6

GCF of 8, 12, 16 is 4

Integers -Adding Integers

If the signs are the same, then add and keep same sign. If signs are different subtract, keep sign of the largest number.

9 + 5 =14 (same sign)
-9 + -5 = -14 (same sign)
-9 + 5 = -4 (opposite signs)

9 + -5 = 4 (opposite signs)

Integers-Dividing Integers

Divide the integers and apply the sign rules.
Same signs = positive answer
Different signs = negative answer

8 ÷ 2 = 4
8 ÷ -2 = -4
-8 ÷ -2 = 4

-8 ÷ 2 = -4

Integers-Multiplying Integers

Multiply the integers and apply the sign rules.
Same signs =positive product
Different signs = negative product

8 * 4 = 32
(-5) * (-2) = 10
5 * (-2) = -10

(-8) * (4) = -32

Inequalities-Solving Inequalities

Step 1 All variables should be on the left of the equal sign and the numbers should be on the right.
Do this by adding opposites
Step 2. Divide by the positive value of the variables coefficient
Step 3. If the coefficient to the variable is negative, reverse the inequality and when dividing by -1 (or any negative).

Step 1 -4b + 6 < -14
Step 2 -6 -6
-4b < -20
Step 3 -b < -5
b > 5

Integers-Subtracting Integers

To subtract an integer add it’s opposite

Apply these rules:

1. Two like signs become positive

2. Two unlike signs become negative

9 - (-4) 9 +(+4) = 13 Two like signs
-9 –(+4) = -9 + -4= -13 Two unlike signs
-9 –(-4) = -9 + (+4) = -5 Two like signs

Inequalities-Writing Inequalities

Use the same rules as writing equations
The < is used instead of “ is less than”
The > is used instead of “ is greater than”

The product of 6 and y is greater than 14

6y > 14 Y more than 6 is less than 11

6 + y < 11

Missing factors

These can be set up as a multiplication problem or a division problem

Monomials-Dividing by a monomials

Separate the expression into two fractions and then divide coefficient but subtract exponents.

(6x² - 4x)/2x (6x²)/2x + (-4x)/2x

3x - 2

Monomials-Dividing monomials

When dividing monomials you subtract the exponents of like variables

(a³ b⁶)⁄(a² b³ )
Divide a’s and b’s

a³⁄a² = a^(3-2)=a

b⁶⁄b³ = b^(6-3)= b³
Combine together ab³

Monomials-Multiplying monomials

When multiplying monomials, add exponents with the same variables

(a² b⁴ c³ )(a³ b⁴ c³) a² x a³= a ⁽²⁺³⁾ =a⁵
b⁴ xb⁴=b⁽⁴⁺⁴⁾ = b⁸
c³ xc³= c⁽³⁺³⁾ = c⁶ combine after adding exponents
a⁵ * b⁸ * c⁶

Monomials-Negative powers of a monomials

When dividing or

multiplying monomials with negative powers use the rules of integers and add the signed numbers.

a⁵ x a^(-3)=a ^(5-3) =a²

b⁴ x b^(-2)=b^(4-2) =b²