Question

Factorise a9+b9+3a6b3+3a3b6

Answer 1

9(a+b)(1+6b)(1+6a) is the answer

Answer 2

Answer:

$(a^3)^3+(b^3)^3+3(a^3)^2b^3+3a^3(b^3)^2 = (a^3+b^3)^3$

Step-by-step explanation:

Given : $a^9+b^9+3a^6b^3+3a^3b^6$

To Find : Factorize

Solution:

$a^9+b^9+3a^6b^3+3a^3b^6$

$(a^3)^3+(b^3)^3+3(a^3)^2b^3+3a^3(b^3)^2$

Identity : $(x+y)^3 =x^3+y^3+3x^2y+3xy^2$

On comparing $x= a^3$ and $y = b^3$

$(a^3)^3+(b^3)^3+3(a^3)^2b^3+3a^3(b^3)^2 = (a^3+b^3)^3$

So, $(a^3)^3+(b^3)^3+3(a^3)^2b^3+3a^3(b^3)^2 = (a^3+b^3)^3$