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Factor x3y6 + 27z42. (xy3 + 3z39)(x2y9 – 3xy3z39 + 9z1,521) (xy3 + 3z39)(x2y6 – 3xy3z39 + 9z78) (x3y6 + 27z42)(x6y12 – 27x3y6z42 + 729z84) (xy2 + 3z14)(x2y4 – 3xy2z14 + 9z28)

Sagot :

MrRoyal

Answer:

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

Step-by-step explanation:

Given

[tex]x^3y^6 + 27z^{42[/tex]

Required

Factor

Express both terms as a cube

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

Let

[tex]a =(xy^2)[/tex]

[tex]b = (3z^{14})[/tex]

So:

[tex]x^3y^6 + 27z^{42} = a^3 + b^3[/tex]

Using sum of cubes:

[tex]a^3 + b^3 = (a + b)(a^2 - ab + b^2)[/tex]

So:

[tex]x^3y^6 + 27z^{42} = (a + b)(a^2 - ab + b^2)[/tex]

Substitute in, values of a and b

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

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

Answer:

its d

Step-by-step explanation:

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