Algebra Formula Cheat Sheet with Identities and Rules

Algebra formula cheat sheet covers important algebra formulas, identities, equations, and expressions, making it easier to simplify problems, solve variables, and understand relationships between numbers in a simple way.

Algebra Formula Cheat Sheet

Topic	Formula	Description
Basic Expression	ax + b	Linear expression
Linear Equation	ax + b = 0	Solve for x
Quadratic Equation	ax² + bx + c = 0	Standard quadratic form
Quadratic Formula	x = (-b ± √(b² − 4ac)) / 2a	Roots of quadratic
Discriminant	D = b² − 4ac	Nature of roots
Sum of Roots	-b/a	Sum of solutions
Product of Roots	c/a	Product of solutions
Identity 1	(a + b)² = a² + 2ab + b²	Square of sum
Identity 2	(a − b)² = a² − 2ab + b²	Square of difference
Identity 3	(a + b)(a − b) = a² − b²	Difference of squares
Identity 4	(a + b)³ = a³ + 3a²b + 3ab² + b³	Cube of sum
Identity 5	(a − b)³ = a³ − 3a²b + 3ab² − b³	Cube of difference
Factorization	a² − b² = (a − b)(a + b)	Basic factorization
Factorization	a³ − b³ = (a − b)(a² + ab + b²)	Difference of cubes
Factorization	a³ + b³ = (a + b)(a² − ab + b²)	Sum of cubes
Slope Formula	(y₂ − y₁)/(x₂ − x₁)	Slope of line
Equation of Line	y = mx + c	Slope-intercept form
Point-Slope Form	y − y₁ = m(x − x₁)	Line through point
Distance Formula	√[(x₂ − x₁)² + (y₂ − y₁)²]	Distance between points
Midpoint Formula	((x₁ + x₂)/2, (y₁ + y₂)/2)	Midpoint of line
Inequality Rule	If a > b then a + c > b + c	Basic inequality
Exponent Rule 1	a^m × a^n = a^(m+n)	Multiply powers
Exponent Rule 2	a^m / a^n = a^(m−n)	Divide powers
Exponent Rule 3	(a^m)^n = a^(mn)	Power of power
Exponent Rule 4	a⁰ = 1	Zero exponent
Log Rule 1	log(ab) = log a + log b	Product rule
Log Rule 2	log(a/b) = log a − log b	Quotient rule
Log Rule 3	log(a^b) = b log a	Power rule

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