Mathematics
stabor0437
13

Which of the following is x⁴ + y⁴ identically equal to? (A) (x² + y²)(x + y)(x - y) (B) (x² + xy + y²)(x² - xy + y²) (C) (x² + √2xy + y²)(x² - √2xy + y²) (D) (x² + √3xy + y²)(x² - √3xy + y²) (E) (x + y)²(x-y)² Can someone explain me how to make it step by step?

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(1) Answers
Gracie216

[latex]x^4+y^4 \\ \\x^4= (x^2)^2, y^4 = (y^2)^2 \\ \\x^4- y^4= (x^2)^2 - (y^2)^2 = (x^2 + y^2)(x^2 - y^2 )\\ \\now \ you \ can \ factor \ the \ second \ again \\ \\(hopefully \ you \ see \ that \ it's \ a \ difference \ of \ squares): \\ \\x^4 - y^4= (x^2 + y^2)(x + y)(x - y) \\ \\Answer : \ (A) \ (x^2 + y^2)(x + y)(x - y) \\ \\ \\ a^2-b^2 =(a-b)(a+b)[/latex]

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