Factor (x^(3/2))-(a^(3/2)).
I know that generally the solution should be (x-a) multiplied by some kind of binomial expansion, but the fractions are throwing me off. Any hints? Thanks.

Question

Factor (x^(3/2))-(a^(3/2)).
I know that generally the solution should be (x-a) multiplied by some kind of binomial expansion, but the fractions are throwing me off. Any hints? Thanks.

cruffo · Answer

Are you familiar with the formula for factoring differences of cubes:

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

cruffo · Answer

Think of this problem as [sqrt(x)]^3 - [sqrt(a)]^3

cruffo · Answer

Does that help?

nikolas · Answer

Thanks! I'd seen the difference of cubes formula before but didn't recognize it here. Need to think about those exponents more carefully next time.