what are the steps to finging out the answer to:a^3-16ab^2?

Question

a cubed minus 16ab squared.

Answer 1

a³ - 16ab²

Factor out the a:

a(a² - 16b²)

The second factor is what is called a "difference of squares".

Whenever you have x² - y², it ALWAYS factors as (x + y)(x - y), which you can verify using FOIL). In this case, x = a and y = 4b, so:

a(a + 4b)(a - 4b)

Answer 2

First, you want to take out any common terms. a is a common term for both, so first factor out an a, giving you
a (a^2 - 16b^2)
Now factor (a^2 - 16b^2)
Notice that you only have two terms; therefore you know that you have to have two factors of -16 that cancel each other out, which would be 4 and -4. Now factor:
(a + 4b) (a - 4b) = a^2 -4ab +4ab - 16b^2
Notice that the 4ab and -4ab cancel out like I said before, giving you a^2 - 16b^2. Now multiply by a giving you
a(a^2 - 16b^2) = a^3 - 16ab^2, so it checks.
a(a + 4b) (a - 4b) is your answer.

Answer 3

Factor out an a, giving
a(a^2-16b^2)
This factors into
a(a + 4b)(a - 4b)

Answer 4

first divide it with an a
a(a^2-16b^2)
then factorise
a(a-4b)(a+4b)

Answer 5

a³-16ab² =
a(a² - 4b²) = a(a-4b)(a+4b)
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