Arithmetic Review

Evaluating Expressions

Simplify Expressions

Exponential Expressions

Factor by GCF

Factoring Polynomials

Factoring Part 2

Factoring Special Cases

Solving Equations

Translating into numerical expressions

Inequalities

Rational Expressions

Complex Fractions

Quadratic Equations

Building the Equation of the line

Graphing Lines

Graphing Inequalities

Absolute Value Inequalities

Absolute Value Equations

Functions

System of Equations

Word Problems

Radical Expressions

Quadratic Functions

Practice Pert Tests

Evaluating Expressions

Simplify Expressions

Exponential Expressions

Factor by GCF

Factoring Polynomials

Factoring Part 2

Factoring Special Cases

Solving Equations

Translating into numerical expressions

Inequalities

Rational Expressions

Complex Fractions

Quadratic Equations

Building the Equation of the line

Graphing Lines

Graphing Inequalities

Absolute Value Inequalities

Absolute Value Equations

Functions

System of Equations

Word Problems

Radical Expressions

Quadratic Functions

Practice Pert Tests

The difference of two squares

a²- b²= (a - b)(a + b)

Sometimes we have special cases of factoring, for example:

X²-1= (X -1)(X+1)

X²- 25 = (X-5)(X+5)

X²- 36 = (X-6)(X+6)

64X²-81Y²=(8X -9Y)(8X+9Y)

Binomials and Trinomials

When we have a binomial, we need to factor it by using these formulas

(a + b)² = a²+ 2ab + b²

(a - b)² = a²-2ab + b²

For example:

(3X + 9)² = (3X)²+ 2(3X)(9)+(9)²= 9X²- 54X + 81

(2X - 3Y)²= (2X)²- 2(2X)(3Y) +(3Y)²= 4X² -12XY + 9Y²

The Cube of a binomial

These are

(a + b)³= a³+ 3a²b + 3ab²+ b³

(a -b)³= a³-3a²b + 3ab²-b³

For example:

(2X + 3)³ = (2X)³+3(2X)²(3) + 3(2X)(3)²+ (3)³

= 8X³+36X² + 54X + 27

(X - 4)³ = X³ -3(X)²4 + 3X(4)²- (4)³ = X³-12X²+ 48X - 64

a²- b²= (a - b)(a + b)

Sometimes we have special cases of factoring, for example:

X²-1= (X -1)(X+1)

X²- 25 = (X-5)(X+5)

X²- 36 = (X-6)(X+6)

64X²-81Y²=(8X -9Y)(8X+9Y)

Binomials and Trinomials

When we have a binomial, we need to factor it by using these formulas

(a + b)² = a²+ 2ab + b²

(a - b)² = a²-2ab + b²

For example:

(3X + 9)² = (3X)²+ 2(3X)(9)+(9)²= 9X²- 54X + 81

(2X - 3Y)²= (2X)²- 2(2X)(3Y) +(3Y)²= 4X² -12XY + 9Y²

The Cube of a binomial

These are

(a + b)³= a³+ 3a²b + 3ab²+ b³

(a -b)³= a³-3a²b + 3ab²-b³

For example:

(2X + 3)³ = (2X)³+3(2X)²(3) + 3(2X)(3)²+ (3)³

= 8X³+36X² + 54X + 27

(X - 4)³ = X³ -3(X)²4 + 3X(4)²- (4)³ = X³-12X²+ 48X - 64