factoring cubes

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how to factor x^3-27

well since 27 is a perfect cube and so is x^3 wouldn't the answer be x-3?

no, its something like (2x-3)(?x^2+?X+?) i don't know how to figure all the parts out.

Here's the format for the difference between two cubes:

(a - b)(a^2 + ba + b^2) = a^3 - b^3.

Using this format for your problem:
a = x, b = 3 (the cubed root of 27 is 3).

(x - 3)(x^2 + 3x + 9) = x^3 - 27

I hope this will help.



yes thank you so much!

oooooo yeah now i remember.

since it is minus the formula should be something like:

(a-b)(a^2 + ab + b^2)

x^3-27

(x-3)(x^2 +3x+ 9)
^^i think that's the answer

how about 8x^3-27? how do you do that?

a=2x
b=3

You can use the same format because the cubed root of 8x^3 is 2x.

Here's the format again for the difference between two cubes:

(a - b)(a^2 + ba + b^2) = a^3 - b^3.

Using the format:
a = 2x, b = 3 (the cubed root of 27 is 3).

(2x - 3)(4x^2 + 6x + 9) = 8x^3 - 27

And there you have it!

Hi Math Guru is there a way to figure out
(a - b)(a^2 + ba + b^2) = a^3 - b^3
without just memorizing the formula?

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