Algebra Overview 📊

Like Terms

Radicals: Like terms must have the same radicand:
- 3√2 + 8√2 + 5√7 + 3√7 → 11√2 + 8√7

Use properties to combine or distribute terms
Addition/Subtraction:
- Add/subtract coefficients of like terms
- Ex: 7x + 4x^2 + 5x + 9x^2 → 13x^2 + 12x
- Distribute negative signs
Multiplication: Distribute each term
- Ex: monomial x trinomial: 7x * (x² + 2x - 3) → 7x³ + 14x² - 21x
- Ex: binomial x binomial: 3x - 4 * 2x + 7 → Apply FOIL method: 6x² + 13x - 28
- Ex: binomial x trinomial: Distribute each term in the binomial across the trinomial

Multiplication: Add exponents
- x³ * x⁴ = x⁷
Division: Subtract exponents
- x⁹ / x⁴ = x⁵
Power of a Power: Multiply exponents
- (x²)³ = x⁶
Negative Exponents: Move base to the opposite part of the fraction
- x^(-3) = 1/x³

Apply multiplication, power rules, and combine like terms
- Ex: (3x³y⁻²)(7x⁻⁸y⁵) → (21x⁻⁵y³) which becomes 21y³/x⁵

Linear equations:
- Isolate x: Ex: 2x + 4 = 9 → x = 2.5
- Combine like terms, move constants to one side, divide to solve for x
Quadratic equations (factoring, quadratic formula):
- Factoring: ax² + bx + c = 0
- Quadratic Formula: x = [-b ± √(b² - 4ac)] / (2a)
- Complete the square method for non-factorable cases

y = mx + b form: m = slope, b = y-intercept
Plot y-intercept, use slope to find another point
Standard Form: Ax + By = C
- Convert to slope-intercept for graphing: y = mx + b

Given a point & slope: Use point-slope form
- y - y1 = m(x - x1)
- Convert to slope-intercept: y = mx + b
Given 2 points: Find slope, use point-slope form
- m = (y2 - y1) / (x2 - x1)

Parallel lines: Same slope
Perpendicular lines: Negative reciprocal slopes (if m1 = a/b, m2 = -b/a)

Practice Problems