已知：A=x²+xy+y²,B=x²-xy+y²,x²+3xy+4y²=2,4x²-2xy+y²=3,求代数式4A+B-（A-B)的值

已知：A=x²+xy+y²,B=x²-xy+y²,x²+3xy+4y²=2,4x²-2xy+y²=3,求代数式4A+B-（A-B)的值
已知：A=x²+xy+y²,B=x²-xy+y²,x²+3xy+4y²=2,4x²-2xy+y²=3,
求代数式4A+B-（A-B)的值

已知：A=x²+xy+y²,B=x²-xy+y²,x²+3xy+4y²=2,4x²-2xy+y²=3,求代数式4A+B-（A-B)的值
4A + B -(A - B)
= 4A + B -A + B
= 3A + 2B
= 3(x^2 + xy + y^2 ) + 2(x^2 -xy + y^2)
= 3x^2 + 3xy + 3y^2 + 2x^2 - 2xy + 2y^2
= 5x^2 + xy + 5y^2
= (x^2 + 3xy + 4y^2) +(4x^2 - 2xy + y^2)
= 2 + 3 = 5

4A+B-(A-B)=4x²+4xy+4y²+x²-xy+y²-(x²+xy+y²-x²+xy-y²)
=5x²+xy+5y²
x²+3xy+4y² +4x²-2xy+y²
=5x²+xy+5y² =5
得 4A+B-(A-B)=5