# A Cube Plus B Cube With Examples

A cube PLUS B Cube ( A^3+B^3) is a Mathematics Formula which is used in its Branch Algebra. When We Start Algebra to understand, We face many Formulae Like A Plus B Whole Square, A Square Minus B Square, A Plus B Whole Cube Etc.

Today I’m Going to Tell You This Famous Formula A Cube Plus Cube. Once You Learn this, You can Solve any problem related to this.

## A Cube PLUS B Cube (A^3+B^3)

A Cube Plus cube Generally known as the sum of cubes. It is used to calculate sum of cubes without actually calculating the cubes.

This formula become easy when you learn it.

A Cube Plus B Cube = ( A Plus B ) ( A Square Minus AB Plus B Square)

A^3+B^3 = (A+B) (A^2-AB+B^2)

### Examples of A Cube Plus Cube

1- 3^3 + 2^3 = (3+2) (3^2 – 3×2 +2^2)

= 5 (9-6+4) = 5×7 = 35

Explanation – Here I assumed 3 in the place of A and 2 in the Place of B. And then I put the value of A and B.

2- 4^3 + 3^3 = (4+3) (4^2-4×3+3^2)

= 7 (16-12+9)

= 7×13 = 91

Explanation- Here I assumed 4 in the place of A and 3 in the place of B. And Then Put value of A and B in the formula.

### Proof of A cube Plus cube (A^3+B^3)

A^3+B^3 = (A+B) (A^2-AB+B^2)

Here I’ll prove LHS and RHS Part is Equal.

RHS = (A+B) (A^2-AB+B^2)

= A^3 – A^2 B + A B^2 + B A^2 – A B^2 + B^3

= A^3 – A^2B+BA^2 + AB^2-AB^2 + B^3

= A^3 + 0 + 0 + B^3

= A^3 + B^3

= LHS

Hence Proved.

Final Words –

So Friends These are formula, examples and Proof of A Cube Plus Cube. And This becomes very easy when you learn it.