How do you simplify (a^3 - b^3)/(3a^2 + 9ab + 6b^2)*(a^2 + 2ab + b^2)/(a^2 - b^2)?

1 Answer
Jul 19, 2015

Factor and cancel matching factors to find:

(a^3-b^3)/(3a^2+9ab+6b^2)*(a^2+2ab+b^2)/(a^2-b^2)=(a^2+ab+b^2)/(3(a+2b))

Explanation:

Use difference of cubes identity:

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

Use difference of squares identity:

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

(a^3-b^3)/(3a^2+9ab+6b^2)*(a^2+2ab+b^2)/(a^2-b^2)

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

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

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