Question

x^4+12x^3y+37x^2y^2+12xy^3+y^4分解因式,急爆了!

Answer 1

x^4 + 12x"'y + 37x"y" + 12xy"' + y^4

= (x")" + 2x"y" + (y")" + 12xy( x" + y" ) + 35x"y"

= ( x" + y" )" + 5xy( x" + y" ) + 7xy( x" + y" ) + 35x"y"

= ( x" + y" )( x" + y" + 5xy ) + 7xy( x" + y" + 5xy )

= ( x" + y" + 5xy )( x" + y" + 7xy )

或者

= (x")" + 2x"y" + (y")" + 12x"'y + 12xy"' + 35x"y"

= ( x" + y" )" + 12xy( x" + y" ) + (6xy)" - 36x"y" + 35x"y"

= ( x" + y" + 6xy )" - x"y"

= ( x" + y" + 5xy )( x" + y" + 7xy )