展開する (4-x)^{1/2}(1+2x)^2

解

展開する

(4 - x)^{\frac{1}{2}} (1 + 2 x)^{2}

(4 - x)^{\frac{1}{2}} + (4 - x)^{\frac{1}{2}} \cdot 4 x + (4 - x)^{\frac{1}{2}} \cdot 4 x^{2}

解答ステップ

(4 - x)^{\frac{1}{2}} (1 + 2 x)^{2}

拡張

(1 + 2 x)^{2} : 1 + 4 x + 4 x^{2}

= (4 - x)^{\frac{1}{2}} (1 + 4 x + 4 x^{2})

分配法則を適用する:

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

(4 - x)^{\frac{1}{2}} (1 + 4 x + 4 x^{2}) = (4 - x)^{\frac{1}{2}} \cdot 1 + (4 - x)^{\frac{1}{2}} \cdot 4 x + (4 - x)^{\frac{1}{2}} \cdot 4 x^{2}

= (4 - x)^{\frac{1}{2}} \cdot 1 + (4 - x)^{\frac{1}{2}} \cdot 4 x + (4 - x)^{\frac{1}{2}} \cdot 4 x^{2}

規則を適用する:

a \cdot 1 = a

(4 - x)^{\frac{1}{2}} \cdot 1 = (4 - x)^{\frac{1}{2}}

= (4 - x)^{\frac{1}{2}} + (4 - x)^{\frac{1}{2}} \cdot 4 x + (4 - x)^{\frac{1}{2}} \cdot 4 x^{2}