# Proof A Cube Minus B Cube Formula

## Proof A Cube Minus B Cube Formula

Are you looking for a Cube minus b Cube Formula? You can check the formulas of a cube minus b Cube in this way. We are going to share the $$a^3 – b^3$$ algebra formulas for you as well as how to create $$a^3 – b^3$$ and proof.

we know that what is the formulas of $$(a-b)^3$$. use the of this formula to prove a cube minus b cube formula.

$$=> (a-b)^3 = a^3 – b^3 – 3ab (a-b)$$

$$=> (a-b)^3 + 3ab (a-b) = a^3 – b^3$$

$$=> a^3 – b^3 = (a-b)^3 + 3ab (a-b)$$ [Note: Take comman part (a-b)]

$$=> a^3 – b^3 = (a-b)((a-b)^2 + 3ab)$$ [use the formula of a minus b whole square]

$$=> a^3 – b^3 = (a-b)(a^2 + b^2 -2ab + 3ab)$$

$$=> a^3 – b^3 = (a-b)(a^2 + b^2 + ab)$$

### Verify $$a^3 – b^3$$ Formula

Need to verify $$a^3 – b^3$$ formula is right or wrong. put the value of a =2 and b=1

put the value of a and b in the LHS

$$=> a^3 – b^3 = 2^3 – 1^3$$

$$=> a^3 – b^3 = 8 – 1 = 7$$

put the value of a and b in the RHS

$$=> (a-b) (a^2+ b^2 + ab)$$

$$=> (2-1) (2^2+ 1^2 + 2 \times 1)$$

$$=> (1) (4+ 1 + 2)$$

$$=> (1) (7) = 7$$

Therefore $$LHS = RHS$$ [LHR = left hand side, RHS = right hand side]

Verify Formula $$=> a^3 – b^3 = (a-b) (a^2+ b^2 + ab)$$

#### Summary $$a^3 – b^3$$

If you have any issues in the $$a^3 – b^3$$ formulas, please let me know through social media and mail. A cube minus B Cube is the most important algebra maths formulas for class 6 to 12.