Question

Factorize this... I have stuck on this...Plz someone help me....Plz show steps also

x^4 - y^4 + x^2 - y^2

Answer 1

✪ Question : x⁴ - y⁴ + x² - y²

✪ Solution : x⁴ - y⁴ + x² - y²

= (x²)² - (y²)² + x² - y²

a² - b² = ( a + b )( a - b )

= ( x² - y² )( x² + y² ) + ( x - y )( x + y )

= ( x - y )( x + y )( x² + y² ) + ( x - y )( x + y )

Taking ( x - y )( x + y ) common,

= [( x - y )( x + y )][( x² + y² ) + 1]

= ( x - y )( x + y )( x² + y² + 1 )

✪ Answer : ( x - y )( x + y )( x² + y² + 1 )