could someone help me understand this concept?

Question

Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box.

 

(a³ −125)/(a²-25)

Answer 1

The numerator is the DIFFERENCE OF CUBES: (a³-5³) = (a-5)(a²+5a+25) and

the denominator is the difference of squares: (a²-5²) = (a-5)(a+5).

 

You should be able to see that when the factored numerator is placed above the factored denominator, the (a-b)

factors will cancel.

 

All of the difference of squares, the difference of cubes and the sum of cubes are factorable.

All Algebra students are advised to learn the pattern of their factorizations, because such expressions will recur throughout all of one's math courses, not just the current one.