Question

For making (x^4 - 11x^2y^2 + y^4) a perfect square,
the expression to be added is :​

Answer 1

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.

Answer 2

Answer:

=> 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)