Question

factorise of x⁴+x²y²+y⁴​

Answer 1

x4 +(x2 × y2 )+y4 + (x2 × y2 )-(x2 × y2)

= x4+ 2(x2 × y2) + y4 - (x2 × y2)

= {(X2)2 + 2 (x2 × y2) + (y2)2 }- (x2 × y2)

The above statement is in the form (a+ b)2= a2 + 2a × b + b2

= {(x2 + y2)2 }- (x2 + y2)

Taking (x2 + y2) common

= (x2 + y2)(x2 +y2 -1)

Answer 2

$x4 \: + \: x2 \: y2 \: + y4 \\ \\ x4 + 2x2y2 \: + \: y4 \: - x2y2 \\ \\ hence \: we \: are \: adding \: and \: subtract \: x2y2 \\ \\ (x2 + y2)2 - \: (xy2) \\ \\ (x2 + y2 + xy) \: \: (x2 + y2 - xy) \\ \\ using \: a2 - b2$