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

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

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expand (1+3x)^5

expand

(1 + 3 x)^{5}

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

Solution steps

(1 + 3 x)^{5}

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{- 24 + 28 i}{- 10 + 6 i}

(11 - 5 i) - (12 + 2 i)

\frac{7}{1}

\frac{2 ^{- 3}}{8 ^{- 1}}

(3 x + 4)^{3}

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