Question

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?

Answer 1

`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)`