Algebraic Expressions

Algebraic expressions are the equations we get when operations such as addition, subtraction, multiplication, division, etc. are operated upon any variable. This tool provides a comprehensive reference of principal algebraic expression formulas.

Formula NumberExpressionResult/SimplificationDescription
(1)a · aa²Multiplication of identical variables
(2)a · a · aa³Multiplication of three identical variables
(3)a · babMultiplication of different variables
(4)a² · b²(ab)²Product of squares
(5)a² · a³a⁵Product rule: a^m · a^n = a^(m+n)
(6)a⁴ / a³aQuotient rule: a^m / a^n = a^(m-n)
(7)a⁰1Any variable to the power of zero equals one
(8)(a + b)²a² + 2ab + b²Square of a sum
(9)(a - b)²a² - 2ab + b²Square of a difference
(10)(a + b)³a³ + 3a²b + 3ab² + b³Cube of a sum
(11)(a - b)³a³ - 3a²b + 3ab² - b³Cube of a difference
(12)a² - b²(a - b)(a + b)Difference of squares
(13)a³ - b³(a - b)³ + 3ab(a - b)Difference of cubes
(14)a³ + b³(a + b)³ - 3ab(a + b)Sum of cubes
(15)ab((a + b)/2)² - ((a - b)/2)²Product as difference of squares
(16)a³ / b³(a / b)³Quotient of cubes
(17)1 / a³(1 / a)³ = a⁻³Reciprocal of a cube
(18)(a²)³a⁶Power of a power: (a^m)^n = a^(mn)
(19)a³ + b³(a + b)(a² - ab + b²)Sum of cubes factorization
(20)a³ - b³(a - b)(a² + ab + b²)Difference of cubes factorization
(21)(a + b)³a³ + 3a²b + 3ab² + b³Cube of sum expansion
(22)(a - b)³a³ - 3a²b + 3ab² - b³Cube of difference expansion
(23)a^(1/2) · a^(1/2)aSquare root multiplication
(24)a^(1/3) · a^(1/3) · a^(1/3)aCube root multiplication
(25)(a^(1/3))³aCube of cube root
(26)(a²)^(1/3)a^(2/3)Fractional exponent rule
(27)(a^(1/3))^(1/4)a^(1/12)Power of fractional exponent
(28)(ab)^(1/3)a^(1/3) · b^(1/3)Cube root of product
(29)(a / b)^(1/3)a^(1/3) / b^(1/3)Cube root of quotient
(30)(1 / a)^(1/3)a^(-1/3)Cube root of reciprocal