Question

x^4– y^4 + x² - y² factorise​

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)

Answer 2

Step-by-step explanation:

$({x}^{4} - {y}^{4} )+ {x}^{2} - {y}^{2} \\ = ( {x}^{2} ) ^{2} - ({ {y}^{2} })^{2} + {x}^{2} - {y}^{2} \\ = ( {x}^{2} + {y}^{2} )( {x}^{2} - {y}^{2} ) + ( {x}^{2} - {y}^{2} ) \\ = {x}^{2} - {y}^{2} (( {x}^{2} + {y}^{2} ) + 1)$