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)} (- 5)^{i}

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{x ^{2} + 5 x}{x ^{2} - 25}

x \times (- 1)

12800

3.14 \cdot 3^{2}

1 3^{5}

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