What is expand (1+3x)^6 ?

The solution to expand (1+3x)^6 is 1+18x+135x^2+540x^3+1215x^4+1458x^5+729x^6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (1+3x)^6

expand

(1 + 3 x)^{6}

1 + 18 x + 135 x^{2} + 540 x^{3} + 1215 x^{4} + 1458 x^{5} + 729 x^{6}

Solution steps

(1 + 3 x)^{6}

Apply binomial theorem:

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

a = 1, b = 3 x

= i = 0 \sum 6 (i 6) \cdot 1^{(6 - i)} (3 x)^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 1^{6} (3 x)^{0} : 1

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 1^{5} (3 x)^{1} : 18 x

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 1^{4} (3 x)^{2} : 135 x^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 1^{3} (3 x)^{3} : 540 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 1^{2} (3 x)^{4} : 1215 x^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 1^{1} (3 x)^{5} : 1458 x^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 1^{0} (3 x)^{6} : 729 x^{6}

= 1 + 18 x + 135 x^{2} + 540 x^{3} + 1215 x^{4} + 1458 x^{5} + 729 x^{6}

4 m + 12

2 x - \frac{1}{x}

(x + 3 y^{3})^{2}

5 x^{2} + 9 x y - 6 x y + 7 y^{2} - x^{2}

What is expand (1+3x)^6 ?
The solution to expand (1+3x)^6 is 1+18x+135x^2+540x^3+1215x^4+1458x^5+729x^6