簡約 (g^2+1/4)(g+1/2)(g-1/2)

解

簡約

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

\frac{( 4 g ^{2} + 1 ) ( 2 g + 1 ) ( 2 g - 1 )}{16}

解答ステップ

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

簡素化

g^{2} + \frac{1}{4} : \frac{4 g ^{2} + 1}{4}

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

分数の規則を適用する:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

簡素化

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

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

分数の規則を適用する:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

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

数を乗じる:

4 \cdot 4 = 16

= \frac{( 4 g ^{2} + 1 ) ( g \cdot 2 + 1 ) ( g \cdot 2 - 1 )}{16}

= \frac{( 4 g ^{2} + 1 ) ( 2 g + 1 ) ( 2 g - 1 )}{16}