GRE Math formula sheet : Algebra

Algebra

Simplifying Expressions

Simplifying expressions:

Multiplying monomials:

Multiplying polynomials using FOIL (First, Outer, Inner, Last)

Factoring

Factoring using Greatest Common Factors:

Factoring using difference of squares:

Factoring using quadratic polynomials:

Combining methods:

Factoring rational expressions (as long as x is not equal to 4):

Solving Equations

The golden rule of solving equations is, “What you do to one side of an equation, you must also do to the other”.

Eliminating fractions:

Multiply by the LCD:

Cross-multiplication:

Quadratic equations:

 Quadratic formula:

Two variables/systems of equations 

Method 1: Substitution

Method 2: Elimination

A system of two equations with two unknowns can have 0, 1, or infinitely many solutions.

To solve a system of three equations with three variables, use substitution to reduce the problem to two equations with two variables, and solve from there.