Question

For making the function g(x) = x⁴ - 8x²y² + y⁴ a perfect square, the expression to be added as:....?​

Answer 1

Answer:

$\huge\bf\underline\red{AnSweR:}$

g(x) = x⁴ - 8x²y² + y⁴

${x}^{4} - 8 {x}^{2} {y}^{2} + {y}^{4 } = ( { {x}^{2} })^{2} - 2 {x}^{2} {y}^{2} + ( { {y}^{2} })^{2} - 6 {x}^{2} {y}^{2}$

$= ( { {x}^{2} - {y}^{2} })^{2} - 6 {x}^{2} {y}^{2}$

So, 6x²y² should be added to make it perfect Square.

$\bf\purple{Hope\:it\: will\:Be\: HelPfuL :)}$

Answer 2

Answer:

HelĺŌ $\huge\red{\ddot\smile}$

=> 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 -c 3xy)

hope help u mate$\huge\red{\ddot\blue}$