展開する (4ax)/((x+a)^2(x-a)^2)

解

展開する

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

\frac{4 a x}{x ^{4} - 2 a ^{2} x ^{2} + a ^{4}}

解答ステップ

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

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

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

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

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

拡張

(x^{2} + 2 x a + a^{2}) (x^{2} - 2 x a + a^{2}) : x^{4} - 2 a^{2} x^{2} + a^{4}

= \frac{4 a x}{x ^{4} - 2 a ^{2} x ^{2} + a ^{4}}