簡約 (m^2n^2-3/4)(m^2n^2+1/2)

解

簡約

(m^{2} n^{2} - \frac{3}{4}) (m^{2} n^{2} + \frac{1}{2})

\frac{( 4 m ^{2} n ^{2} - 3 ) ( 2 m ^{2} n ^{2} + 1 )}{8}

解答ステップ

(m^{2} n^{2} - \frac{3}{4}) (m^{2} n^{2} + \frac{1}{2})

簡素化

m^{2} n^{2} - \frac{3}{4} : \frac{4 m ^{2} n ^{2} - 3}{4}

= \frac{4 m ^{2} n ^{2} - 3}{4} (m^{2} n^{2} + \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 m ^{2} n ^{2} - 3 ) ( m ^{2} n ^{2} + \frac{1}{2} )}{4}

簡素化

(4 m^{2} n^{2} - 3) (m^{2} n^{2} + \frac{1}{2}) : \frac{( 4 m ^{2} n ^{2} - 3 ) ( m ^{2} n ^{2} \cdot 2 + 1 )}{2}

= \frac{\frac{( 4 m ^{2} n ^{2} - 3 ) ( m ^{2} n ^{2} \cdot 2 + 1 )}{2}}{4}

分数の規則を適用する:

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

= \frac{( 4 m ^{2} n ^{2} - 3 ) ( m ^{2} n ^{2} \cdot 2 + 1 )}{2 \cdot 4}

数を乗じる:

2 \cdot 4 = 8

= \frac{( 4 m ^{2} n ^{2} - 3 ) ( m ^{2} n ^{2} \cdot 2 + 1 )}{8}

= \frac{( 4 m ^{2} n ^{2} - 3 ) ( 2 m ^{2} n ^{2} + 1 )}{8}