Math Doubts

${(a-b)}^3$ formula

Formula

${(a-b)}^3$ $\,=\,$ $a^3-b^3-3ab(a-b)$

Introduction

$a$ and $b$ are taken as two terms, then the difference of them is a binomial $a-b$. The cube of difference of them is written mathematically as cube of a binomial $a-b$. It is read as $a$ minus $b$ whole cube. It is actually used as a formula to expand cube of difference of any two terms in terms of them as follows.

${(a-b)}^3$ $\,=\,$ $a^3-b^3-3a^2b+3ab^2$

Proofs

The $a$ minus $b$ whole cube identity can be proved mathematically in two different mathematical approaches.

Algebraic method

Learn how to derive the expansion of $a$ minus $b$ whole cubed identity by the product of three same difference basis binomials.

Geometric method

Learn how to derive the expansion of $a$ minus $b$ whole cube formula geometrically by the volume of a cube.



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