What is expand (x-pi)^5 ?

The solution to expand (x-pi)^5 is x^5-5pix^4+10pi^2x^3-10pi^3x^2+5pi^4x-pi^5

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expand (x-pi)^5

expand

(x - π)^{5}

x^{5} - 5 π x^{4} + 10 π^{2} x^{3} - 10 π^{3} x^{2} + 5 π^{4} x - π^{5}

Solution steps

(x - π)^{5}

Apply binomial theorem:

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

a = x, b = - π

= i = 0 \sum 5 (i 5) x^{(5 - i)} (- π)^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} x^{5} (- π)^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} (- π)^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} (- π)^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} (- π)^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} (- π)^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} (- π)^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} x^{5} (- π)^{0} : x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} (- π)^{1} : - 5 π x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} (- π)^{2} : 10 π^{2} x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} (- π)^{3} : - 10 π^{3} x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} (- π)^{4} : 5 π^{4} x

\frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} (- π)^{5} = - π^{5}

= x^{5} - 5 π x^{4} + 10 π^{2} x^{3} - 10 π^{3} x^{2} + 5 π^{4} x - π^{5}

(x - π)^{6}

\frac{x ( x - 1 )}{20}

\frac{( 9 x - 2 ) ^{3}}{7}

\frac{1}{v ( m - 3 )}

- 2 (2 z + 1 = 26)

What is expand (x-pi)^5 ?
The solution to expand (x-pi)^5 is x^5-5pix^4+10pi^2x^3-10pi^3x^2+5pi^4x-pi^5