What is expand (a-6)^4 ?

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

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expand (a-6)^4

expand

(a - 6)^{4}

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

Solution steps

(a - 6)^{4}

Apply binomial theorem:

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

a = a, b = - 6

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

(x - 2 y)^{6}

\frac{5}{15 b - b}

5 x y (x + 1) + 10 x (x + 1)

24 x^{2} \cdot y + 36 x^{3} \cdot y^{2} - 12 x^{4} \cdot y^{3}

((15 0^{y})^{2})^{3}

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