Question

factorise a^9 + b^9 + 3a^6 b^3 + 3a^3 b^6

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The factorization of  $a^9 + b^9 + 3a^6 b^3 + 3a^3 b^6$  is $(a^3+b^3)^3$.

Explanation:

Polynomial identity : $x^3+y^3+3x^2y+3xy^2= (x+y)^3$   (1)

The given expression : $a^9 + b^9 + 3a^6 b^3 + 3a^3 b^6$

This expression can be rewritten as : $=a^{3\times3}+b^{3\times3}+3a^{3\times2}b^3+3a^3b^{3\times2}\\\\=(a^3)^3 + (b^3)^3 + 3(a^3)^2 (b^3) + 3(a^3) (b^3)^2\ \ [\text{Identity in exponents\ }(a^m)^n=a^{mn}]$

$= (a^3+b^3)^3\ \ \ \ [\text{By using (1)}]$

Hence, the factorization of  $a^9 + b^9 + 3a^6 b^3 + 3a^3 b^6$  is $(a^3+b^3)^3$.

# Learn more :

Factorize : a(a+b)³-3a²b(a+b)

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