Question

p^3-216q^3

Answer 1

Do you want the answer?

Answer 2

Or do want to know what the 'p' and 'q' stand for?

Answer 3

Use the identity
\(\Large a^3 - b^3 = (a-b)(a^2 + ab + b^2)\)

Answer 4

Sorry, yes, I do want the answer :)

Answer 5

Okay give me sec

Answer 6

k

Answer 7

Do you want it simplified?

Answer 8

I am not completely sure, it just says to factor it.

Answer 9

\(\Large p^3 - 216q^3 = p^3 - (6q)^3\)

Compare this to the identity I gave before. a = p and b = 6q.
Plug it into the right hand side of the identity and simplify.

Answer 10

Where is the 6 coming from?

Answer 11

6 x 6 x 6 = 216.
So 216 = 6^3

Answer 12

\( \Large
a^3 - b^3 = (a-b)(a^2 + ab + b^2) \\ \Large
p^3 - (6q)^3 = (p - 6q)(p^2 + p(6q) + (6q)^2) \\ \Large
~~~~~~~~~~~~~~~~~= (p - 6q)(p^2 + 6pq + 36q^2)
\)

Answer 13

I went on a calculator but the only thing it gave was this: p^3+-216q^3

Answer 14

Sorry :(

Answer 15

If you factor p^3-216q^3 you get (p-6q)(p^2 + 6pq + 36q^2) as shown above.
If there is any part that you don't follow let me know.

Answer 16

Okay, Thank you both so so much for your help :). So so much :)

Answer 17

yw.

Answer 18

You're welcome! :)