zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

展开 (3t-4/(sqrt(p)))^5

解答

展开

(3 t - \frac{4}{p})^{5}

解答

243 t^{5} - \frac{1620 t ^{4}}{p} + \frac{4320 t ^{3}}{p} - \frac{5760 t ^{2}}{p p} + \frac{3840 t}{p ^{2}} - \frac{1024}{p ^{2} p}

求解步骤

(3 t - \frac{4}{p})^{5}

使用二项式定理:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 3 t, b = - \frac{4}{p}

= i = 0 \sum 5 (i 5) (3 t)^{(5 - i)} (- \frac{4}{p})^{i}

展开求和

= \frac{5 !}{0 ! ( 5 - 0 ) !} (3 t)^{5} (- \frac{4}{p})^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (3 t)^{4} (- \frac{4}{p})^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (3 t)^{3} (- \frac{4}{p})^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (3 t)^{2} (- \frac{4}{p})^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (3 t)^{1} (- \frac{4}{p})^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (3 t)^{0} (- \frac{4}{p})^{5}

化简

\frac{5 !}{0 ! ( 5 - 0 ) !} (3 t)^{5} (- \frac{4}{p})^{0} : 243 t^{5}

化简

\frac{5 !}{1 ! ( 5 - 1 ) !} (3 t)^{4} (- \frac{4}{p})^{1} : - \frac{1620 t ^{4}}{p}

化简

\frac{5 !}{2 ! ( 5 - 2 ) !} (3 t)^{3} (- \frac{4}{p})^{2} : \frac{4320 t ^{3}}{p}

化简

\frac{5 !}{3 ! ( 5 - 3 ) !} (3 t)^{2} (- \frac{4}{p})^{3} : - \frac{5760 t ^{2}}{( p ) ^{3}}

化简

\frac{5 !}{4 ! ( 5 - 4 ) !} (3 t)^{1} (- \frac{4}{p})^{4} : \frac{3840 t}{p ^{2}}

化简

\frac{5 !}{5 ! ( 5 - 5 ) !} (3 t)^{0} (- \frac{4}{p})^{5} : - \frac{1024}{( p ) ^{5}}

= 243 t^{5} - \frac{1620 t ^{4}}{p} + \frac{4320 t ^{3}}{p} - \frac{5760 t ^{2}}{( p ) ^{3}} + \frac{3840 t}{p ^{2}} - \frac{1024}{( p ) ^{5}}

化简

243 t^{5} - \frac{1620 t ^{4}}{p} + \frac{4320 t ^{3}}{p} - \frac{5760 t ^{2}}{( p ) ^{3}} + \frac{3840 t}{p ^{2}} - \frac{1024}{( p ) ^{5}} : 243 t^{5} - \frac{1620 t ^{4}}{p} + \frac{4320 t ^{3}}{p} - \frac{5760 t ^{2}}{p p} + \frac{3840 t}{p ^{2}} - \frac{1024}{p ^{2} p}

= 243 t^{5} - \frac{1620 t ^{4}}{p} + \frac{4320 t ^{3}}{p} - \frac{5760 t ^{2}}{p p} + \frac{3840 t}{p ^{2}} - \frac{1024}{p ^{2} p}

流行的例子

展开 1/((x+5)^2)

e x p an d \frac{1}{( x + 5 ) ^{2}}

展开 s/((s+3)(s+5))

e x p an d \frac{s}{( s + 3 ) ( s + 5 )}

化简 (a+ib)^3

s im pl i f y (a + ib)^{3}

展开 x^{2/3}(x-2)

e x p an d x^{\frac{2}{3}} (x - 2)

化简 (2+3i)^5

s im pl i f y (2 + 3 i)^{5}