What is expand (x-9)^4 ?

The solution to expand (x-9)^4 is x^4-36x^3+486x^2-2916x+6561

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expand (x-9)^4

expand

(x - 9)^{4}

x^{4} - 36 x^{3} + 486 x^{2} - 2916 x + 6561

Solution steps

(x - 9)^{4}

Apply binomial theorem:

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

a = x, b = - 9

= i = 0 \sum 4 (i 4) x^{(4 - i)} (- 9)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} (- 9)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (- 9)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (- 9)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (- 9)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (- 9)^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} (- 9)^{0} : x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (- 9)^{1} : - 36 x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (- 9)^{2} : 486 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (- 9)^{3} : - 2916 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (- 9)^{4} : 6561

= x^{4} - 36 x^{3} + 486 x^{2} - 2916 x + 6561

(x + 1)^{2} + 2 (x + 1)

7 (2 p + 2 q)

- \frac{7}{10} + \frac{7}{50}

4 x^{3} - 19 x^{2} + 21 x

\frac{2 ^{4}}{4 ^{2}}

What is expand (x-9)^4 ?
The solution to expand (x-9)^4 is x^4-36x^3+486x^2-2916x+6561