展開する cos(x^2+2xy+y^2)(2y+2x)(x+y)

解

展開する

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})

解答ステップ

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

拡張

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})

分配法則を適用する:

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})