展开 cos(x^2+2xy+y^2)(2y+2x)(x+y)

解答

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cos (x^{2} + 2 x y + y^{2}) (2 y + 2 x) (x + y)

4 x y cos (x^{2} + 2 x y + y^{2}) + 2 y^{2} cos (x^{2} + 2 x y + y^{2}) + 2 x^{2} cos (x^{2} + 2 x y + y^{2})

求解步骤

cos (x^{2} + 2 x y + y^{2}) (2 y + 2 x) (x + y)

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cos (x^{2} + 2 x y + y^{2}) (2 y + 2 x) (x + y) : cos (x^{2} + 2 x y + y^{2}) (4 x y + 2 y^{2} + 2 x^{2})

= cos (x^{2} + 2 x y + y^{2}) (4 x y + 2 y^{2} + 2 x^{2})

使用分配律:

m (a + b + c) = ma + mb + m c

cos (x^{2} + 2 x y + y^{2}) (4 x y + 2 y^{2} + 2 x^{2}) = cos (x^{2} + 2 x y + y^{2}) \cdot 4 x y + cos (x^{2} + 2 x y + y^{2}) \cdot 2 y^{2} + cos (x^{2} + 2 x y + y^{2}) \cdot 2 x^{2}

= cos (x^{2} + 2 x y + y^{2}) \cdot 4 x y + cos (x^{2} + 2 x y + y^{2}) \cdot 2 y^{2} + cos (x^{2} + 2 x y + y^{2}) \cdot 2 x^{2}

= 4 x y cos (x^{2} + 2 x y + y^{2}) + 2 y^{2} cos (x^{2} + 2 x y + y^{2}) + 2 x^{2} cos (x^{2} + 2 x y + y^{2})

s im pl i f y x^{\frac{2}{3}} (\frac{5}{2} - x)

e x p an d 7 (9 + 2)

e x p an d y (y - 3)

e x p an d \frac{2 x ^{3} + 5 x ^{2} + 4 x}{( x + 1 ) ^{2}}

e x p an d \frac{1}{s ( e ^{- 2 L s} + 1 ) ( e ^{- L s} + 1 )}