What is expand (x+5)^5 ?

The solution to expand (x+5)^5 is x^5+25x^4+250x^3+1250x^2+3125x+3125

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expand (x+5)^5

expand

(x + 5)^{5}

x^{5} + 25 x^{4} + 250 x^{3} + 1250 x^{2} + 3125 x + 3125

Solution steps

(x + 5)^{5}

Apply binomial theorem:

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

a = x, b = 5

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

Expand summation

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

Simplify

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

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} \cdot 5^{1} : 25 x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} \cdot 5^{2} : 250 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} \cdot 5^{3} : 1250 x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} \cdot 5^{4} : 3125 x

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} \cdot 5^{5} : 3125

= x^{5} + 25 x^{4} + 250 x^{3} + 1250 x^{2} + 3125 x + 3125

12 x - 6

(x - 4)^{3}

\frac{2}{3} \div \frac{1}{5}

(4 x - 3) (3 x^{2} - 2 x + 1)

64 \frac{1}{2}

What is expand (x+5)^5 ?
The solution to expand (x+5)^5 is x^5+25x^4+250x^3+1250x^2+3125x+3125