Basic Algebra Formulas with Examples
A complete guide to the fundamental algebra formulas. Each formula includes a clear explanation and a worked example so you can understand and apply it immediately.
1. Linear Equation in One Variable
The standard form of a linear equation in one variable is ax + b = 0, where a and b are constants and x is the unknown.
Solution: x = -b / a
Example: Solve 3x + 6 = 0
3x + 6 = 0
3x = -6
x = -6 / 3 = -2
2. Quadratic Formula
For any quadratic equation ax² + bx + c = 0(where a ≠ 0), the solutions are given by the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Example:Solve x² - 5x + 6 = 0
a = 1, b = -5, c = 6
x = (5 ± √(25 - 24)) / 2
x = (5 ± 1) / 2
x = 3 or x = 2
3. Difference of Squares
The difference of two perfect squares can always be factored:
a² - b² = (a + b)(a - b)
Example:Factor x² - 9
x² - 9 = x² - 3²
= (x + 3)(x - 3)
4. Binomial Expansion (a + b)²
The square of a binomial follows this pattern:
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
Example:Expand (x + 4)²
(x + 4)² = x² + 2(x)(4) + 4²
= x² + 8x + 16
5. Slope of a Line
The slope mof a line passing through two points (x₁, y₁) and (x₂, y₂):
m = (y₂ - y₁) / (x₂ - x₁)
Example: Find the slope of a line through (1, 3) and (4, 9)
m = (9 - 3) / (4 - 1)
m = 6 / 3 = 2
6. Slope-Intercept Form
The equation of a line in slope-intercept form:
y = mx + b
where m = slope, b = y-intercept
Example: Write the equation of a line with slope 2 passing through (1, 3)
y = mx + b
3 = 2(1) + b
b = 1
y = 2x + 1
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