ALGEBRA

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

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  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.

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  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!

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