已知：A=2x^2-3xy+2y^2,B=2x^2+xy-3y^2 求①A+B ②A-(B-2A)

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已知：A=2x^2-3xy+2y^2,B=2x^2+xy-3y^2 求①A+B ②A-(B-2A)
已知：A=2x^2-3xy+2y^2,B=2x^2+xy-3y^2 求①A+B ②A-(B-2A)

已知：A=2x^2-3xy+2y^2,B=2x^2+xy-3y^2 求①A+B ②A-(B-2A)
A=2x^2-3xy+2y^2,B=2x^2+xy-3y^2 求①A+B ②A-(B-2A)
①A+B =2x^2-3xy+2y^2+2x^2+xy-3y^2
=4x^2-2xy-y^2
②A-(B-2A)
=A-B+2A
=3A-B
=3(2x^2-3xy+2y^2)-(2x^2+xy-3y^2 )
=6x^2-9xy+6y^2-2x^2-xy+3y^2
=4x^2-10xy+9y^2

A+B
=(2x^2-3xy+2y^2)+(2x^2+xy-3y^2)
=2x^2-3xy+2y^2+2x^2+xy-3y^2
=4x^2-2xy-y^2
A-(B-2A)
=A-B+2A
=3A-B
=3(2x^2-3xy+2y^2)+(2x^2+xy-3y^2)
=6x^2-9xy+6y^2+2x^2+xy-3y^2
=8x^2-8xy+3y^2

A+B = 2x^2-3xy+2y^2+2x^2+xy-3y^2
=4x^2 - 2xy - y^2
A-(B-2A) = 3A-B
=3(2x^2-3xy+2y^2) - (2x^2+xy-3y^2)
=6x^2 -9xy +6y^2 - 2x^2 - xy + 3y^2
=4x^2 -10xy +9y^2

A+B=4x^2-2xy-y^2 A-(B-2A)=3A-B=4x^2-10xy+9y^2

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