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Factor The Polynomial Using A Special Factorization. X^(6)+27y^(3)

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Sure, let's do this.

When looking at the polynomial x^6 + 27y^3, one might recognize it as a sum of cubes. Generally speaking, sum of cubes can be represented by (a^3 + b^3) and factored using the formula (a + b)(a^2 − ab + b^2).

Here, we can rewrite the polynomial appropriately, to fit the formula, as follows:

(x^6 + (3y)^3), where 'a' is x^2 (note that (x^2)^3 = x^6) and 'b' is 3y.

Therefore, we can apply the formula to get the factored polynomial:

Using (a + b)(a^2 − ab + b^2), we'd substitute x^2 for 'a', and 3y for 'b' to get:
(x^2 + 3y)(x^4 - 3x^2*y + 9y^2)

That then is the factored form of the polynomial x^6 + 27y^3.

User Amanpreet Kaur
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