The formula for the cube of the difference of two terms aaa and bbb, known as the (a - b) whole cube formula , is:
(a−b)3=a3−3a2b+3ab2−b3(a-b)^3=a^3-3a^2b+3ab^2-b^3(a−b)3=a3−3a2b+3ab2−b3
This formula expands the cube of the binomial a−ba-ba−b by multiplying (a−b)(a−b)(a−b)(a-b)(a-b)(a-b)(a−b)(a−b)(a−b) and simplifying the terms. It is useful for quickly calculating or factorizing expressions involving the cube of a difference
Summary of the (a - b)³ formula:
- Cube of the first term: a3a^3a3
- Minus three times the product of the square of the first term and the second term: −3a2b-3a^2b−3a2b
- Plus three times the product of the first term and the square of the second term: +3ab2+3ab^2+3ab2
- Minus the cube of the second term: −b3-b^3−b3
This identity is an important algebraic tool for expanding or factoring cubic expressions involving the difference of two terms
