What is expand (x-5)^6 ?

The solution to expand (x-5)^6 is x^6-30x^5+375x^4-2500x^3+9375x^2-18750x+15625

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expand (x-5)^6

expand

(x - 5)^{6}

x^{6} - 30 x^{5} + 375 x^{4} - 2500 x^{3} + 9375 x^{2} - 18750 x + 15625

Solution steps

(x - 5)^{6}

Apply binomial theorem:

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

a = x, b = - 5

= i = 0 \sum 6 (i 6) x^{(6 - i)} (- 5)^{i}

Expand summation

= \frac{6 !}{0 ! ( 6 - 0 ) !} x^{6} (- 5)^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} x^{5} (- 5)^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} x^{4} (- 5)^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} x^{3} (- 5)^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} x^{2} (- 5)^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} x^{1} (- 5)^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} x^{0} (- 5)^{6}

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} x^{6} (- 5)^{0} : x^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} x^{5} (- 5)^{1} : - 30 x^{5}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} x^{4} (- 5)^{2} : 375 x^{4}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} x^{3} (- 5)^{3} : - 2500 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} x^{2} (- 5)^{4} : 9375 x^{2}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} x^{1} (- 5)^{5} : - 18750 x

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} x^{0} (- 5)^{6} : 15625

= x^{6} - 30 x^{5} + 375 x^{4} - 2500 x^{3} + 9375 x^{2} - 18750 x + 15625

(x - 1) (x + 8)

16 x^{2} - 16 x + 4

72 x^{5} 2

(x y - 3 z) (2 x y + 5 z)

lo g_{4} (128) - lo g_{4} (2)

What is expand (x-5)^6 ?
The solution to expand (x-5)^6 is x^6-30x^5+375x^4-2500x^3+9375x^2-18750x+15625