What is expand (3+x)^5 ?

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

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expand (3+x)^5

expand

(3 + x)^{5}

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

Solution steps

(3 + x)^{5}

Apply binomial theorem:

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

a = 3, b = x

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

20 \div \frac{5}{6}

- 8 \cdot - 2

2 x^{2} (3 x^{5})^{2}

0 + 4

2 (n + 2 n)

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