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.

A Cube Plus B Cube

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)

Proof of A Cube Plus B Cube, A^3+B^3, A3+B3
Proof of A Cube Plus B Cube

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

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

Let’s Start With RHS.

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


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.

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