簡約 (x^4-y^4)/(x-y)

解

簡約

\frac{x ^{4} - y ^{4}}{x - y}

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

解答ステップ

\frac{x ^{4} - y ^{4}}{x - y}

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

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

= \frac{( x ^{2} ) ^{2} - ( y ^{2} ) ^{2}}{x - y}

2乗の差の公式を適用する:

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

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

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

2乗の差の公式を適用する:

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

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

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

共通因数を約分する:

x - y

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