Math Doubts

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

Formula

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

Introduction

If $a$ and $b$ are two terms, then the sum of them is denoted by a binomial $a+b$. The cube of sum of two terms is written in mathematical form as the cube of binomial $a+b$. It is read as $a$ plus $b$ whole cube and it is used as a formula to expand cube of sum of any two terms in terms of them in mathematics.

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

Proofs

The cube of $a$ plus $b$ identity can be proved mathematically in two different methods.

Algebraic method

Learn how to derive the expansion of $a$ plus $b$ whole cube formula by the product of three same sum basis binomials.

Geometric method

Learn how to derive the expansion of $a$ plus $b$ whole cube identity geometrically from volume of a cube.



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