展開する (2r^2+2a^2)/((r+a)^2(r-a)^2)

解

展開する

\frac{2 r ^{2} + 2 a ^{2}}{( r + a ) ^{2} ( r - a ) ^{2}}

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

解答ステップ

\frac{2 r ^{2} + 2 a ^{2}}{( r + a ) ^{2} ( r - a ) ^{2}}

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

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

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

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

拡張

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

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