Question

factorize - x^4+y^4-11x^2y^2

Answer 1

=x^4+y^4-11x^2y^2

=x^2y^2(x^2 - y^2 - 11)

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Answer 2

Answer:

Let u=x2 and v=y2. Then x4−11x2y2+y4=u2−11uv+v2. Given the middle term is not even, then it doesn't factor into something resembling (u+v)2 or (u−v)2. Also, there doesn't appear to be any factors such that ab=1 (the coefficient of the third term) and a+b=−11 (the coefficient of the second term) where u2−11uv+v2 resembles (u±a)(v±b) and the final answer.

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Step-by-step explanation:

=> x⁴ - 11x²y² + y⁴

=> x⁴ - 2x²y² - 9x²y² + y⁴

=> x⁴ - 2x²y² + y⁴ - 9x²y²

=> (x²)² - 2*x²*y² + (y²)² - (3xy)²

=> (x² - y²)² - (3xy)²

=> (x² - y² + 3xy)(x² - y² - 3xy)