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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Yes, there is a way to derive the formula without solely relying on memorization. To understand how to derive it, let's start by expanding the expression on the right side of the equation, a^3 - b^3:
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
Now, let's expand the right side using the distributive property:
(a - b)(a^2 + ab + b^2) = a(a^2 + ab + b^2) - b(a^2 + ab + b^2)
Expanding further:
= a^3 + a^2b + ab^2 - a^2b - ab^2 - b^3
The a^2b and -a^2b terms cancel each other out, and the ab^2 and -ab^2 terms also cancel each other out. Therefore, we are left with:
= a^3 - b^3
Hence, by expanding the expression on the right side, we were able to derive the formula (a - b)(a^2 + ab + b^2) = a^3 - b^3. This method helps us understand the logic behind the formula, rather than relying on memorization alone.