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Algebra Formulas Cheat Sheet page 3

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Algebra Formula cheat sheet

Monomials-Raising monomials to a power

Multiply the exponent in the parentheses by the power.

( a2 b4 c3 )2
(a2)2=
a4
(b4)2=b8
(c3)2=
c6
Combine after multiplying by the power
a4 b8c6

Multiplying signed numbers

 

The Rules

(+) • (+) = (+)
(+) • (-) = (-)
(-) • (+) = (-)
(-) • (-) = (+)

 

Order of Operations

PEMDAS Parentheses

Exponents

Multiply/Divide(left to right)

Add Subtract (left to right)

Plotting points on the coordinate plane

Step 1 Start at the origin. Find the x-axis, count right for positive and left for negative x value
Step 2 Find the y-axis, count up for positive and down for negative y value.
Step 3 Write the location of this point

Plot (6 -4)

 

Step 1 Begin at (0,0) move 6 to the right
If it was negative you would move to the left
Step 2. Move down since it is negative
Step 3 Plot the point

Polynomial multiplied by -1

When you multiply by -1 you simply change the sign of every term listed.

-1(4a + 3b - 3c) = -4a -3b + 3a

 

Polynomial multiplied by a monomial

Multiply each term by the monomial Combine terms

2x(3x2 + 2x -3)
2x(3x2) =
6x3
2x(2x) =
4x2
2x(-3) = -6x
Combine any like and

list from largest exponent in order:

 

6x3 + 4x2 -6

Polynomial multiplied by a variable

Step 1 Multiply each term by the variable remember to add the exponents.

 

Step 2 Combine.


x(3x2 + 2x -3)


x(32)
= 3x3
x(2x) =
2x2
x(-3) = -3x
Combine
3x3 + 2x2 -3x

Polynomial multiplied by an integer

Step 1: Multiply each term by the integer changing only the coefficients.

 

Step 2: Combine terms


2(3x2 + 2x -3)
2(3x2) =
6x2
2(2x) =
4x
2(-3) = -6
Combine 6x^2 + 4x -6

Polynomials-Adding Polynomials

Step 1 Arrange in descending order of exponents Step 2 Combine terms with like variables and exponents

Combine -3x8-6x9-4x9+8x+7x8-2x Step1 6x9-4x9 + 3x8 - 7x8 + 8x - 2x

Step 2 2x9+ 4x8+ 6x

Polynomials-Degree of a polynomial

The highest exponent after being simplified

24 – 53 – 10x + 7 is a fourth degree polynomial

27 – 53 – 102 + 7 is a seventh degree polynomial

Polynomials-Subtracting Polynomials

Set up the problem vertically in descending order
Change the bottom signs and add

15x3 - 10x2 + 3- (10x3 + 30x2 + 2) ......................................................

15x3 - 10x2 + 3
-(10x3+ 30x2 + 2) ............................................................

15x3 - 10x2 + 3
-10x3 - 30x2 - 2
­­­­­­­­­­­­­­­­­­­­­­________________

5x3 - 40x2 + 1

Property-Associative property

a + (b + c) = (a + b) + c

Changing groupings

Ex. 2 + (5 + 3) = (2 + 5) + 3

Property-Commutative property

a + b = b + a

Ex. 7 + 3 = 3 + 7

Property-Distributive property

Multiply the terms inside the parenthesis by the term on the outside of the parenthesis

c(a + b) = ca + cb
3(c - b) = 3c -3b

Quadratic Equation

ax2 + bx + c = 0 a, b, and c are known values x =variable

3x2 + 4x + 3 =0

 

Free Algebra Cheetsheet with over 40 Algebra Formulas.