What is expand (x-pi)^4 ?

The solution to expand (x-pi)^4 is x^4-4pix^3+6pi^2x^2-4pi^3x+pi^4

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expand (x-pi)^4

expand

(x - π)^{4}

x^{4} - 4 π x^{3} + 6 π^{2} x^{2} - 4 π^{3} x + π^{4}

Solution steps

(x - π)^{4}

Apply binomial theorem:

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

a = x, b = - π

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (- π)^{4} = π^{4}

= x^{4} - 4 π x^{3} + 6 π^{2} x^{2} - 4 π^{3} x + π^{4}

\frac{7 x ^{3} + 16 x ^{2} + 20 x + 5}{( x ^{2} + 2 x + 2 ) ^{2}}

(x - \frac{1}{2}) (x + \frac{3}{4})

(cos (θ) + 1)^{2}

(x + i y)^{3} - 2 (x + i y)

What is expand (x-pi)^4 ?
The solution to expand (x-pi)^4 is x^4-4pix^3+6pi^2x^2-4pi^3x+pi^4