The value of $(a + b)^{3} + (a - b)^{3} + 6 a (a^{2} - b^{2})$

6 a^{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

8 a^{3}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

10 a^{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

12 a^{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $8 a^{3}$
Given, $(a + b)^{3} + (a - b)^{3} + 6 a (a^{2} - b^{2})$
Using. $(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)$
$(a + b)^{3} = a^{3} - b^{3} - 3 a b (a - b)$
$a^{2} - b^{2} = (a + b) (a - b)$
$= a^{3} + b^{3} + 3 a^{2} b + 3 b^{2} a + a^{3} - b^{3} - 3 a^{2} b + 3 b^{2} a + 6 a^{3} - 6 a b^{2}$
$= 8 a^{3} + 6 b^{2} a - 6 b^{2} a$
$= 8 a^{3}$
Option B is correct.

Suggest Corrections

Similar questions

(a + b)^{3} + (a - b)^{3} + 6 a (a^{2} - b^{2}) =

(a + b)^{3} + (a - b)^{3} + 6 a (a^{2} - b^{2})

Factorise

(a+b)³+(a-b)3+6a(a²-b²⁾

(a + b)^{3} + (a - b)^{3} + 6 a (a^{2} - b^{2})

Factorise: $8 a^{3} - b^{3} - 12 a^{2} b + 6 a b^{2}$

Join BYJU'S Learning Program