展開する (log_{10}(3)[(x+y)^2])/([x^2+y^2])

解

展開する

\frac{lo g _{10} ( 3 ) [ ( x + y ) ^{2} ]}{[ x ^{2} + y ^{2} ]}

\frac{lo g _{10} ( 3 ) x ^{2} + 2 lo g _{10} ( 3 ) x y + lo g _{10} ( 3 ) y ^{2}}{x ^{2} + y ^{2}}

解答ステップ

\frac{lo g _{10} ( 3 ) ( ( x + y ) ^{2} )}{x ^{2} + y ^{2}}

括弧を削除する:

(a) = a

= \frac{lo g _{10} ( 3 ) ( x + y ) ^{2}}{x ^{2} + y ^{2}}

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

= \frac{lo g _{10} ( 3 ) ( x ^{2} + 2 x y + y ^{2} )}{x ^{2} + y ^{2}}

拡張

lo g_{10} (3) (x^{2} + 2 x y + y^{2}) : lo g_{10} (3) x^{2} + 2 lo g_{10} (3) x y + lo g_{10} (3) y^{2}

= \frac{lo g _{10} ( 3 ) x ^{2} + 2 lo g _{10} ( 3 ) x y + lo g _{10} ( 3 ) y ^{2}}{x ^{2} + y ^{2}}