What is expand (5y^2-z)^5 ?

The solution to expand (5y^2-z)^5 is 3125y^{10}-3125y^8z+1250y^6z^2-250y^4z^3+25y^2z^4-z^5

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expand (5y^2-z)^5

expand

(5 y^{2} - z)^{5}

3125 y^{10} - 3125 y^{8} z + 1250 y^{6} z^{2} - 250 y^{4} z^{3} + 25 y^{2} z^{4} - z^{5}

Solution steps

(5 y^{2} - z)^{5}

Apply binomial theorem:

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

a = 5 y^{2}, b = - z

= i = 0 \sum 5 (i 5) (5 y^{2})^{(5 - i)} (- z)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (5 y^{2})^{5} (- z)^{0} : 3125 y^{10}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (5 y^{2})^{4} (- z)^{1} : - 3125 y^{8} z

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (5 y^{2})^{3} (- z)^{2} : 1250 y^{6} z^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (5 y^{2})^{2} (- z)^{3} : - 250 y^{4} z^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (5 y^{2})^{1} (- z)^{4} : 25 y^{2} z^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (5 y^{2})^{0} (- z)^{5} : - z^{5}

= 3125 y^{10} - 3125 y^{8} z + 1250 y^{6} z^{2} - 250 y^{4} z^{3} + 25 y^{2} z^{4} - z^{5}

7 x + x^{2}

- 980

(- 8 + i) 2

\frac{2}{x} d x

What is expand (5y^2-z)^5 ?
The solution to expand (5y^2-z)^5 is 3125y^{10}-3125y^8z+1250y^6z^2-250y^4z^3+25y^2z^4-z^5