Question

factorise of x⁴+x²y²+y⁴​

Answer 1

Answer:

x^4 +(x^2*y^2 )+y^4 + (x^2*y^2 )-(x^2*y^2)

=x^4+ 2(x^2*y^2) + y^4 - (x^2*y^2)

= {(X^2)^2 + 2 (x^2*y^2) + (y^2)^2 }- (x^2* y^2)

The above statement is in the form (a+ b)^2= a^2 + 2a*b +b^2

= {(x^2 + y^2)^2 }- (x^2 + y^2)

Taking (x^2 + y^2) common

= (x^2 + y^2)(x^2 +y^2 -1)

hope it helps you

Answer 2

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