# Sum and Difference of a Cube

## Sum and Difference of a Cube

You can factorize expressions of form a3 + b3 and a3 - b3 into simpler forms using the algebraic identities sum and difference of cubes. When simplifying algebraic expressions and resolving equations, these identities are helpful.

## Here you can see the sum and difference of cube identities:

• Sum of cubes: a^3 + b^3 = (a + b)(a^2 - ab + b^2)
• Difference of cubes: a^3 - b^3 = (a - b)(a^2 + ab + b^2)

These identities can be obtained by extending the expressions on the right and comparing them with the expressions on the left.

As an example, to factorize the expression x^3 + 8^3, the sum of cubes identity can be used:

x^3 + 8^3 = (x + 8)(x^2 - 8x + 8^2) = (x + 8)(x^2 - 8x + 64)

To simplify algebraic expressions or to solve equations you can use these identities. As an example, to find the value of x that satisfies the equation x^3 + 8^3 = 0, the sum of cubes identity can be used to write:

x^3 + 8^3 = (x + 8)(x^2 - 8x + 64) = 0

This equation can be expressed as (x + 8) = 0 or (x^2 - 8x + 64) = 0. Once you solve these equations singly it will give you x = -8 and x = 4, which are the original equation solutions.