Question

HOW DO YOU FACTOR A^3-27. PLEASE EXPLAIN IN DETAIL

Answer 1

it follows the difference of cubes pattern

A^3 - B^3 = (A-B)(A^2 + AB + b^2)

so (A-3)(.......)

tell me what you got.

Answer 2

We have a difference of cubes.

Did you apply the formula given by Reiny?

If you did, there should be no more doubts.

A^3 - 27 = difference of cubes.

First, write 27 as an exponent.

What number when multiplied by itself 3 times will yield 27?

How about 3?

So, 3 x 3 x 3 = 27, right? This can be written 3^3.

We now have this:

A^3 - 3^3

Next, we apply the rule given to you by Reiny.

A^3 - B^3 = (A-B)(A^2 + AB + b^2)

Here, A = A and B = 3.

We plug and chug.

A^3 - 3^3 = (A - 3)(A^2 + 3A + 3^2)

A^3 - 3^3 = (A - 3)(A^2 + 3A + 9)

Done!