What is expand (3x-sqrt(2))^5 ?

The solution to expand (3x-sqrt(2))^5 is 243x^5-405sqrt(2)x^4+540x^3-180sqrt(2)x^2+60x-4sqrt(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (3x-sqrt(2))^5

expand

(3 x - 2)^{5}

243 x^{5} - 4052 x^{4} + 540 x^{3} - 1802 x^{2} + 60 x - 42

Solution steps

(3 x - 2)^{5}

Apply binomial theorem:

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

a = 3 x, b = - 2

= i = 0 \sum 5 (i 5) (3 x)^{(5 - i)} (- 2)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (3 x)^{5} (- 2)^{0} : 243 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (3 x)^{4} (- 2)^{1} : - 4052 x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (3 x)^{3} (- 2)^{2} : 540 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (3 x)^{2} (- 2)^{3} : - 1802 x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (3 x)^{1} (- 2)^{4} : 60 x

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (3 x)^{0} (- 2)^{5} : - 42

= 243 x^{5} - 4052 x^{4} + 540 x^{3} - 1802 x^{2} + 60 x - 42

\frac{\partial}{\partial x} ((z) (x y + yz + z x - 1))

\frac{18818 + 10864 3}{( 2 + 3 ) ^{4}}

- 3 ((4, 0, - 8) - 8 (6, - 1, - 4))

\frac{( y ^{4} - 1 ) ^{2}}{4 y ^{4}}

\frac{( 3 n ) ( 3 n + 1 )}{( 3 n - 1 ) ( 3 n + 2 )}

What is expand (3x-sqrt(2))^5 ?
The solution to expand (3x-sqrt(2))^5 is 243x^5-405sqrt(2)x^4+540x^3-180sqrt(2)x^2+60x-4sqrt(2)