What is expand (5y-1)^5 ?

The solution to expand (5y-1)^5 is 3125y^5-3125y^4+1250y^3-250y^2+25y-1

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expand (5y-1)^5

expand

(5 y - 1)^{5}

3125 y^{5} - 3125 y^{4} + 1250 y^{3} - 250 y^{2} + 25 y - 1

Solution steps

(5 y - 1)^{5}

Apply binomial theorem:

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

a = 5 y, b = - 1

= i = 0 \sum 5 (i 5) (5 y)^{(5 - i)} (- 1)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (5 y)^{5} (- 1)^{0} : 3125 y^{5}

Simplify

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

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (5 y)^{3} (- 1)^{2} : 1250 y^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (5 y)^{2} (- 1)^{3} : - 250 y^{2}

Simplify

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

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (5 y)^{0} (- 1)^{5} : - 1

= 3125 y^{5} - 3125 y^{4} + 1250 y^{3} - 250 y^{2} + 25 y - 1

\frac{4}{9} + \frac{1}{25}

\frac{n ^{\frac{3}{2}}}{n ^{2}}

x^{2} + \frac{16}{x}

4 x - 6 - 4 x

(\frac{4}{7})^{0}

What is expand (5y-1)^5 ?
The solution to expand (5y-1)^5 is 3125y^5-3125y^4+1250y^3-250y^2+25y-1