What is expand (x+5)^6 ?

The solution to expand (x+5)^6 is x^6+30x^5+375x^4+2500x^3+9375x^2+18750x+15625

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expand (x+5)^6

expand

(x + 5)^{6}

x^{6} + 30 x^{5} + 375 x^{4} + 2500 x^{3} + 9375 x^{2} + 18750 x + 15625

Solution steps

(x + 5)^{6}

Apply binomial theorem:

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

a = x, b = 5

= i = 0 \sum 6 (i 6) x^{(6 - i)} \cdot 5^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} x^{6} \cdot 5^{0} : x^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} x^{5} \cdot 5^{1} : 30 x^{5}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} x^{4} \cdot 5^{2} : 375 x^{4}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} x^{3} \cdot 5^{3} : 2500 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} x^{2} \cdot 5^{4} : 9375 x^{2}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} x^{1} \cdot 5^{5} : 18750 x

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} x^{0} \cdot 5^{6} : 15625

= x^{6} + 30 x^{5} + 375 x^{4} + 2500 x^{3} + 9375 x^{2} + 18750 x + 15625

6 x^{2} - 4 x - 16

\frac{3}{5} - \frac{9}{16}

\frac{35}{4}

- 4 \cdot (- 12)

(7 - 5 i) (2 + 3 i)

What is expand (x+5)^6 ?
The solution to expand (x+5)^6 is x^6+30x^5+375x^4+2500x^3+9375x^2+18750x+15625