因式分解：4x^4+6x^2y-9y^4-9y^3
问题描述：
因式分解：4x^4+6x^2y-9y^4-9y^3
答
4(x^4) + 6x"y - 9(y^4) - 9y"'
= (2x")" - (3y")" + 6x"y - 9y"'
= ( 2x" + 3y" )( 2x" - 3y" ) + 3y( 2x" - 3y" )
= ( 2x" + 3y" + 3y )( 2x" - 3y" )
= ( 2x" + 3y" + 3y )[ (√2)x + (√3)y ][ (√2)x - (√3)y ]
答
4x^4+6x^2y-9y^4-9y^3=4x^4-9y^4 +6x²y-9y³=(2x²+3y²)(2x²-3y²)+3y(2x²-3y²)=(2x²-3y²)(2x²+3y²+3y)