Question

X^6+27 разложить множители , please this solver...

Answer 1

$x^6+27=(x^2)^3+3^3=\\\\\star \; \; a^3+b^3=(a+b)(a^2-ab+b^2)\; \; \star \\\\=(x^2+3)(x^4-3x^2+9)$

Answer 2

X⁶+27=(х²+3)(х⁴-3х²+9)

Answer 3

Sure, I'd be happy to help you factor the expression x^6 + 27.

The given expression x^6 + 27 is a sum of two cubes, where 27 can be written as 3^3. The sum of two cubes can be factored using the formula:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

In this case, a is x^2 and b is 3, so we have:

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

Now, we can further factor the second term using the difference of squares formula (a^2 - b^2 = (a + b)(a - b)):

x^4 - 3x^2 + 9 = (x^2 + 3)(x^2 - 3)

So, the complete factorization of x^6 + 27 is:

x^6 + 27 = (x^2 + 3)(x^2 - 3)(x^2 + 3)

Please double-check the solution and let me know if there's anything else I can assist you with!