What is expand (3x+1)^5 ?

The solution to expand (3x+1)^5 is 243x^5+405x^4+270x^3+90x^2+15x+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (3x+1)^5

expand

(3 x + 1)^{5}

243 x^{5} + 405 x^{4} + 270 x^{3} + 90 x^{2} + 15 x + 1

Solution steps

(3 x + 1)^{5}

Apply binomial theorem:

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

a = 3 x, b = 1

= i = 0 \sum 5 (i 5) (3 x)^{(5 - i)} \cdot 1^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (3 x)^{5} \cdot 1^{0} : 243 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (3 x)^{4} \cdot 1^{1} : 405 x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (3 x)^{3} \cdot 1^{2} : 270 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (3 x)^{2} \cdot 1^{3} : 90 x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (3 x)^{1} \cdot 1^{4} : 15 x

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (3 x)^{0} \cdot 1^{5} : 1

= 243 x^{5} + 405 x^{4} + 270 x^{3} + 90 x^{2} + 15 x + 1

\frac{3}{2}

(\frac{4 x y ^{3}}{x ^{2}})^{2}

2 q^{2} - 8

\frac{- 9}{( - 27 )}

(\frac{1}{3})^{12}

What is expand (3x+1)^5 ?
The solution to expand (3x+1)^5 is 243x^5+405x^4+270x^3+90x^2+15x+1