# Proof A Cube Plus B Cube Formula

## Proof A Cube Plus B Cube Formula

Are you looking for a Cube plus b Cube Formula? You can check the formulas of a cube plus b Cube in this ways. 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 plus 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)]

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

we know that formula of $$(a+b)^2 =a^2+ b^2 + 2ab$$

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

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

### 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=3

put the value of a and b in the LHS

$$=> a^3 + b^3 = 2^3 + 3^3$$

$$= > a^3 + b^3 = 8 + 27 = 35$$

put the value of a and b in the RHS

$$=> (a+b) (a^2+ b^2 – ab)$$

$$=> (2+3) (2^2+ 3^2 -2 \times 3)$$

$$=> (5) (4+ 9 – 6)$$

$$=> (5) (7) = 35$$

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 $$a^3 + b^3$$

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