What is expand (5z-x)^5 ?

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

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expand (5z-x)^5

expand

(5 z - x)^{5}

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

Solution steps

(5 z - x)^{5}

Apply binomial theorem:

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

a = 5 z, b = - x

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

(r^{2})^{2}

5 x^{2} - 20 x - 5

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

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

2 p^{2} + 7 p - 9

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