Question

Factorize 216x^3 + 64y^3

Answer 1

8( 3x+2y) ( 9x^2 -6xy +4y^2)

Explanation:

216x^3 + 64y^3

Factor out the greatest common factor of 8

8( 27x^3 +8y^3)

Rewriting

8 ( (3x)^3 + (2y)^2))

Recognizing this as the difference of cubes)

a^3 + b^3 = (a+b) (a^2-ab+b^2)

8 ( (3x)^3 + (2y)^2)) = 8( 3x+2y) ( 9x^2 -(3x)(2y) +4y^2)

=8( 3x+2y) ( 9x^2 -6xy +4y^2)