What is expand (r-9)^4 ?

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

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expand (r-9)^4

expand

(r - 9)^{4}

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

Solution steps

(r - 9)^{4}

Apply binomial theorem:

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

a = r, b = - 9

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{15 m ^{3} n ^{2}}{3 mn}

200 x y z^{3}

16 x^{3} + 64 x^{2} - 9 x - 36

\frac{( 2 x y ) ^{2}}{( - 2 x y ) ^{3}}

x^{3} + 5 x - 3 x^{2} - 15

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