4x^4+11x^2y^2+9y^4 因式分解

4x^4+11x^2y^2+9y^4 因式分解
4x^4+11x^2y^2+9y^4 因式分解

4x^4+11x^2y^2+9y^4 因式分解
4x⁴+11x²y²+9y⁴因式分解
4x⁴+11x²y²+9y⁴=(2x²+3y²)²-x²y²=(2x²+xy+3y²)(2x²-xy+3y²)=(2x²+xy+3y²)(2x-3y)(x+y)

=（2x+3y）^2-（xy）^2=(2x+3y-xy)(2x+3y-xy)

4(x^4) + 11x"y" + 9(y^4)
= (2x")" + 6x"y" + (3y")" + 6x"y" - x"y"
= 2x"( 2x" + 3y" ) + 3y"( 3y" + 2x" ) - x"y"
= ( 2x" + 3y" )" - (xy)"
= ( 2x" + 3y" + xy )( 2x" + 3y" - xy )
= ( 2x" + xy + 3y" )( 2x" - xy + 3y" )