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Factor x3y6 + 27z42.



A. (xy3 + 3z39)(x2y9 – 3xy3z39 + 9z1,521)


B. (xy3 + 3z39)(x2y6 – 3xy3z39 + 9z78)


C. (x3y6 + 27z42)(x6y12 – 27x3y6z42 + 729z84)


D. (xy2 + 3z14)(x2y4 – 3xy2z14 + 9z28

Respuesta :

The given Polynomial is

[tex]x^3y^6 + 27z^{42}=(x y^2)^3 + (3 z ^{14})^3\\\\ (x y^2+ 3 z^{14})[(x y^2)^2 +(3 z^{14})^2-(xy^2)(3z^{14})]\\\\ (x y^2+ 3 z^{14})[x^2 y^4 +9 z^{28}-3 x y^2z^{14}][/tex]

We have used here the Identity to factorize the polynomial:

a³ + b³= (a+b)(a²+b² - ab)

The Option (D)[tex](xy^2 + 3z^{14})(x^2y^4 - 3xy^2z^{14} + 9 z^{28}][/tex] is correct.

Answer:

D is the correct answer

Step-by-step explanation:

just did the question