it

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popolare Algebra >

espandere (5x+7)^8

Soluzione

espandere

(5 x + 7)^{8}

Soluzione

390625 x^{8} + 4375000 x^{7} + 21437500 x^{6} + 60025000 x^{5} + 105043750 x^{4} + 117649000 x^{3} + 82354300 x^{2} + 32941720 x + 5764801

Fasi della soluzione

(5 x + 7)^{8}

Applicare il teorema binomiale:

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

a = 5 x, b = 7

= i = 0 \sum 8 (i 8) (5 x)^{(8 - i)} \cdot 7^{i}

Espandere la sommatoria

= \frac{8 !}{0 ! ( 8 - 0 ) !} (5 x)^{8} \cdot 7^{0} + \frac{8 !}{1 ! ( 8 - 1 ) !} (5 x)^{7} \cdot 7^{1} + \frac{8 !}{2 ! ( 8 - 2 ) !} (5 x)^{6} \cdot 7^{2} + \frac{8 !}{3 ! ( 8 - 3 ) !} (5 x)^{5} \cdot 7^{3} + \frac{8 !}{4 ! ( 8 - 4 ) !} (5 x)^{4} \cdot 7^{4} + \frac{8 !}{5 ! ( 8 - 5 ) !} (5 x)^{3} \cdot 7^{5} + \frac{8 !}{6 ! ( 8 - 6 ) !} (5 x)^{2} \cdot 7^{6} + \frac{8 !}{7 ! ( 8 - 7 ) !} (5 x)^{1} \cdot 7^{7} + \frac{8 !}{8 ! ( 8 - 8 ) !} (5 x)^{0} \cdot 7^{8}

Semplificare

\frac{8 !}{0 ! ( 8 - 0 ) !} (5 x)^{8} \cdot 7^{0} : 390625 x^{8}

Semplificare

\frac{8 !}{1 ! ( 8 - 1 ) !} (5 x)^{7} \cdot 7^{1} : 4375000 x^{7}

Semplificare

\frac{8 !}{2 ! ( 8 - 2 ) !} (5 x)^{6} \cdot 7^{2} : 21437500 x^{6}

Semplificare

\frac{8 !}{3 ! ( 8 - 3 ) !} (5 x)^{5} \cdot 7^{3} : 60025000 x^{5}

Semplificare

\frac{8 !}{4 ! ( 8 - 4 ) !} (5 x)^{4} \cdot 7^{4} : 105043750 x^{4}

Semplificare

\frac{8 !}{5 ! ( 8 - 5 ) !} (5 x)^{3} \cdot 7^{5} : 117649000 x^{3}

Semplificare

\frac{8 !}{6 ! ( 8 - 6 ) !} (5 x)^{2} \cdot 7^{6} : 82354300 x^{2}

Semplificare

\frac{8 !}{7 ! ( 8 - 7 ) !} (5 x)^{1} \cdot 7^{7} : 32941720 x

Semplificare

\frac{8 !}{8 ! ( 8 - 8 ) !} (5 x)^{0} \cdot 7^{8} : 5764801

= 390625 x^{8} + 4375000 x^{7} + 21437500 x^{6} + 60025000 x^{5} + 105043750 x^{4} + 117649000 x^{3} + 82354300 x^{2} + 32941720 x + 5764801

Esempi popolari

semplificare sqrt(-43)

s im pl i f y - 43

semplificare-2x*(-x)

s im pl i f y - 2 x \cdot (- x)

espandere (9x-4)(9x+4)

e x p an d (9 x - 4) (9 x + 4)

semplificare (6y^3)/(2x^{-2)y^3}

s im pl i f y \frac{6 y ^{3}}{2 x ^{- 2} y ^{3}}

semplificare ln(((3x(2x-1)^{1/3})/((5-x)^2))^{2/3})

s im pl i f y ln (\frac{3 x ( 2 x - 1 ) ^{\frac{1}{3}}}{( 5 - x ) ^{2}})^{\frac{2}{3}}