Question

先化简再求值：(2x+y)^2-(2x+y)(3x-y)-2(3x-y)^2；其中x=-2，y=-1

Answer 1

(2x+y)^2-(2x+y)(3x-y)-2(3x-y)^2；其中x=-2，y=-1
解 设（2x+y）=a, (3x-y)=b.
则原式可化为：a2-ab-2b2=(a+b)(a-2b)---------①
将（2x+y）=a, (3x-y)=b代入①中得：
原式=5x(3y-4x) -------②
将x=-2，y=-1代入②得：原式=-50

Answer 2

解：原式=（2x+y)(2x+y-3x+y)-2(9x²-6xy+y²)
=(2x+y)(-x+2y)-18x²+12xy-2y²
=-2x²+4xy-xy+2y²-18x²+12xy-2y²
=-20x²+15xy
当x=-2，y=-1时
原式=-20*4 +15*2
=-80+30
=-50

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Answer 3

(2x+y)^2-(2x+y)(3x-y)-2(3x-y)^2
=4x²+4xy+y²-6x²-xy+y²-18x²+12xy-2y²
=-15x²+15xy
=-15x(x-y)
=-15x-2x(-2+1)
=-30

Answer 4

原式=-20x^2+15xy
代入=50

Answer 5

-50

Answer 6

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

=5x(5x+2y)-5x(3x-y)
=5x(2x+3y)
=10X7
=70

Answer 7

=4x^2+4xy+y^2-6x^2-xy+y^2-18x^2+12xy+2y^2
=-20x^2+15xy+4y^2
代入x=-2，y=-1，得
-20*(-2)^2+15*(-2)*(-1)+4*(-1)^2=-46