Question

Factor 27a^3 b^9+8c^18

Answer 1

Answer:

(3ab^3+2c^6)(9a^2b^6-6ab^3c^6+4c^12)

Step-by-step explanation:

Given:

Polynomial 27a^3 b^9+8c^18

Factoring the given polynomial

27a^3b^9 can be written as

=3^3.a^3.b^3^3

=(3ab^3)^3

Also 8c^18 can be written as

=2^3.c^6^3

=(2c^6)^3

Hence Polynomial 27a^3 b^9+8c^18 can be written as

=(3ab^3)^3+(2c^6)^3

Applying sum of cubes formula i.e. a^3 + b^3=(a+b)(a^2 – ab + b^2)

=(3ab^3+2c^6)(9a^2b^6-6ab^3c^6+4c^12) !