Question

Factorize X^4 + y ^ 4 + X2 y2

Answer 1

Question :-

Factorize - x⁴ + y⁴ + x²y²

Answer :-

$\sf {x}^{4} + {y}^{4} + {x}^{2} {y}^{2}$

$\sf = {x}^{4} + {y}^{4} + {x}^{2} {y}^{2} + {x}^{2} {y}^{2} - {x}^{2} {y}^{2}$

$\sf = ({x}^{4} + {y}^{4} + 2 {x}^{2} {y}^{2} ) - ( {x}^{2} {y}^{2} )$

$\sf = [(x^2)^2 + (y^2)^2 + 2 (x^2)(y^2) ]( {x}^{2} {y}^{2} )$

$\sf =({x}^{2} + {y}^{2}) ^{2} - {(xy)}^{2}$

$\sf = ({x}^{2} + {y}^{2} + xy)( {x}^{2} + {y}^{2} - xy)$