Factorise $a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}$

Open in App

Solution

$a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}$
$(a - b)^{3} = a^{3} - b^{3} - 3 a b (a - b)$
$\Rightarrow a^{3} - b^{3} - 3 a^{2} b + 3 a b^{2}$
Compairing both polynomials we get,
$∴ a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3} = (a - b)^{3}$

Suggest Corrections

Similar questions

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

Which of the following is an expansion of the identity ${(a - b)}^{3}$ ?

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

Join BYJU'S Learning Program