What is expand (x-6)^4 ?

The solution to expand (x-6)^4 is x^4-24x^3+216x^2-864x+1296

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expand (x-6)^4

expand

(x - 6)^{4}

x^{4} - 24 x^{3} + 216 x^{2} - 864 x + 1296

Solution steps

(x - 6)^{4}

Apply binomial theorem:

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

a = x, b = - 6

= i = 0 \sum 4 (i 4) x^{(4 - i)} (- 6)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} (- 6)^{0} : x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (- 6)^{1} : - 24 x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (- 6)^{2} : 216 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (- 6)^{3} : - 864 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (- 6)^{4} : 1296

= x^{4} - 24 x^{3} + 216 x^{2} - 864 x + 1296

8 a^{3} - 27 b^{6}

\frac{- 11 π}{3}

(6 x - 4) (2 x - 7)

(2 + 3 i) \cdot (4 + 5 i)

(\frac{9}{- 10}) (\frac{6}{- 7})

What is expand (x-6)^4 ?
The solution to expand (x-6)^4 is x^4-24x^3+216x^2-864x+1296