展開する ((8xA+16xt+xA^2)^2)/(4A^2)

解

展開する

\frac{( 8 x A + 16 x t + x A ^{2} ) ^{2}}{4 A ^{2}}

\frac{x ^{2} A ^{2}}{4} + 16 x^{2} + 4 x^{2} A + \frac{64 x ^{2} t}{A} + \frac{64 x ^{2} t ^{2}}{A ^{2}} + 8 x^{2} t

解答ステップ

\frac{( 8 x A + 16 x t + x A ^{2} ) ^{2}}{4 A ^{2}}

(8 x A + 16 x t + x A^{2})^{2} = x^{2} A^{4} + 64 x^{2} A^{2} + 16 x^{2} A^{3} + 256 x^{2} A t + 256 x^{2} t^{2} + 32 x^{2} A^{2} t

= \frac{x ^{2} A ^{4} + 64 x ^{2} A ^{2} + 16 x ^{2} A ^{3} + 256 x ^{2} A t + 256 x ^{2} t ^{2} + 32 x ^{2} A ^{2} t}{4 A ^{2}}

分数の規則を適用する:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{2} A ^{4} + 64 x ^{2} A ^{2} + 16 x ^{2} A ^{3} + 256 x ^{2} A t + 256 x ^{2} t ^{2} + 32 x ^{2} A ^{2} t}{4 A ^{2}} = \frac{x ^{2} A ^{4}}{4 A ^{2}} + \frac{64 x ^{2} A ^{2}}{4 A ^{2}} + \frac{16 x ^{2} A ^{3}}{4 A ^{2}} + \frac{256 x ^{2} A t}{4 A ^{2}} + \frac{256 x ^{2} t ^{2}}{4 A ^{2}} + \frac{32 x ^{2} A ^{2} t}{4 A ^{2}}

= \frac{x ^{2} A ^{4}}{4 A ^{2}} + \frac{64 x ^{2} A ^{2}}{4 A ^{2}} + \frac{16 x ^{2} A ^{3}}{4 A ^{2}} + \frac{256 x ^{2} A t}{4 A ^{2}} + \frac{256 x ^{2} t ^{2}}{4 A ^{2}} + \frac{32 x ^{2} A ^{2} t}{4 A ^{2}}

\frac{x ^{2} A ^{4}}{4 A ^{2}} = \frac{x ^{2} A ^{2}}{4}

\frac{64 x ^{2} A ^{2}}{4 A ^{2}} = 16 x^{2}

\frac{16 x ^{2} A ^{3}}{4 A ^{2}} = 4 x^{2} A

\frac{256 x ^{2} A t}{4 A ^{2}} = \frac{64 x ^{2} t}{A}

\frac{256 x ^{2} t ^{2}}{4 A ^{2}} = \frac{64 x ^{2} t ^{2}}{A ^{2}}

\frac{32 x ^{2} A ^{2} t}{4 A ^{2}} = 8 x^{2} t

= \frac{x ^{2} A ^{2}}{4} + 16 x^{2} + 4 x^{2} A + \frac{64 x ^{2} t}{A} + \frac{64 x ^{2} t ^{2}}{A ^{2}} + 8 x^{2} t