What is expand (x+2pi)^4 ?

The solution to expand (x+2pi)^4 is x^4+8pix^3+24pi^2x^2+32pi^3x+16pi^4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (x+2pi)^4

expand

(x + 2 π)^{4}

x^{4} + 8 π x^{3} + 24 π^{2} x^{2} + 32 π^{3} x + 16 π^{4}

Solution steps

(x + 2 π)^{4}

Apply binomial theorem:

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

a = x, b = 2 π

= i = 0 \sum 4 (i 4) x^{(4 - i)} (2 π)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} (2 π)^{0} : x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (2 π)^{1} : 8 π x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (2 π)^{2} : 24 π^{2} x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (2 π)^{3} : 32 π^{3} x

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (2 π)^{4} = 16 π^{4}

= x^{4} + 8 π x^{3} + 24 π^{2} x^{2} + 32 π^{3} x + 16 π^{4}

- (\frac{8 x}{y} - \frac{w}{t})^{2}

(12 x^{(3)} + 6 x^{(2)} - 2 x + 3) d x

(2 a - (x - c)^{2} + y^{2})^{2}

\frac{( 1 - sin ( x ) + t ^{2} ) t}{( 1 + t ^{2} ) ^{2}}

What is expand (x+2pi)^4 ?
The solution to expand (x+2pi)^4 is x^4+8pix^3+24pi^2x^2+32pi^3x+16pi^4