簡約 (a^4-b^4)/(a-b)

解

簡約

\frac{a ^{4} - b ^{4}}{a - b}

(a^{2} + b^{2}) (a + b)

解答ステップ

\frac{a ^{4} - b ^{4}}{a - b}

a^{4} = (a^{2})^{2}

b^{4} = (b^{2})^{2}

= \frac{( a ^{2} ) ^{2} - ( b ^{2} ) ^{2}}{a - b}

2乗の差の公式を適用する:

x^{2} - y^{2} = (x + y) (x - y)

(a^{2})^{2} - (b^{2})^{2} = (a^{2} + b^{2}) (a^{2} - b^{2})

= \frac{( a ^{2} + b ^{2} ) ( a ^{2} - b ^{2} )}{a - b}

2乗の差の公式を適用する:

x^{2} - y^{2} = (x + y) (x - y)

a^{2} - b^{2} = (a + b) (a - b)

= \frac{( a ^{2} + b ^{2} ) ( a + b ) ( a - b )}{a - b}

共通因数を約分する:

a - b

= (a^{2} + b^{2}) (a + b)