Factors of $(a + b)^{3} - (a - b)^{3}$ are

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

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

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

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

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

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

3 a^{2} + b^{2}

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

Open in App

Solution

The correct option is C $2 b (3 a^{2} + b^{2})$
$(a + b)^{3} - (a - b)^{3}$
$\Rightarrow a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} - (a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3})$
$\Rightarrow a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} - a^{3} + 3 a^{2} b - 3 a b^{2} + b^{3}$
$\Rightarrow 6 a^{2} b + 2 b^{3}$
$\Rightarrow 2 b (3 a^{2} + b^{2})$

Suggest Corrections

Similar questions

(a + b)^{2}

(a - b)^{2}

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

(a + b)^{3}

(a - b)^{3}

a^{3} + b^{3}

a^{3} - b^{3}

b_{1}, b_{2}, b_{3}, . . . b_{n}

b_{1} b_{2} + b_{2} b_{3} + b_{3} b_{4} + . . . + b_{n - 1} b_{n} =

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

a^{3} b^{2}, a^{2} b^{3}, b^{2} a^{3}, b^{3} a^{2} .

(a - b) : (a + b), (a - b)^{2} : (a + b)^{2}

(a + b)^{3} : (a - b)^{3}

Join BYJU'S Learning Program