Question

计算 求过程 完全平方公式、平方差公式

(3x+y)^2-2(3x+y)(3x-y)+(3x-y)^2
(4x+3y)(3y-4x)-(3x-2y)(3x+2y)
(2x-y)^2-（2x+y）^2-(x+y)(2x-y)

Answer 1

(3x+y)^2-2(3x+y)(3x-y)+(3x-y)^2
=[(3x+y)-(3x-y)]^2
=(2y)^2
=4y^2

(4x+3y)(3y-4x)-(3x-2y)(3x+2y)
=9y^2-16x^2-(9x^2-4y^2)
=-25x^2+13y^2

(2x-y)^2-（2x+y）^2-(x+y)(2x-y)
=[(2x-y)+(2x+y)][(2x-y)-(2x+y)]-(x+y)(2x-y)
=4x*(-2y)-(x+y)(2x-y)
=-8xy-(2x^2+xy-y^2)
=-2x^2-9xy+y^2

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