What is expand (-(piL^2(90-arccos(2/L)))/(360)-4)^2 ?

The solution to expand (-(piL^2(90-arccos(2/L)))/(360)-4)^2 is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (-(piL^2(90-arccos(2/L)))/(360)-4)^2

expand

(- \frac{π L ^{2} ( 90 - arccos ( \frac{2}{L} ) )}{360} - 4)^{2}

\frac{π ^{2} L ^{4}}{16} - \frac{π ^{2} L ^{4} arccos ( \frac{2}{L} )}{720} + \frac{π ^{2} L ^{4} arccos ^{2} ( \frac{2}{L} )}{129600} + 2 π L^{2} - \frac{π L ^{2} arccos ( \frac{2}{L} )}{45} + 16

Solution steps

(- \frac{π L ^{2} ( 90 - arccos ( \frac{2}{L} ) )}{360} - 4)^{2}

Expand

π L^{2} (90 - arccos (\frac{2}{L})) : 90 π L^{2} - π L^{2} arccos (\frac{2}{L})

= (- \frac{90 π L ^{2} - π L ^{2} arccos ( \frac{2}{L} )}{360} - 4)^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = - \frac{90 π L ^{2} - π L ^{2} arccos ( \frac{2}{L} )}{360}, b = 4

= (- \frac{90 π L ^{2} - π L ^{2} arccos ( \frac{2}{L} )}{360})^{2} - 2 (- \frac{90 π L ^{2} - π L ^{2} arccos ( \frac{2}{L} )}{360}) \cdot 4 + 4^{2}

Simplify

(- \frac{90 π L ^{2} - π L ^{2} arccos ( \frac{2}{L} )}{360})^{2} - 2 (- \frac{90 π L ^{2} - π L ^{2} arccos ( \frac{2}{L} )}{360}) \cdot 4 + 4^{2} : \frac{8100 π ^{2} L ^{4} - 180 π ^{2} L ^{4} arccos ( \frac{2}{L} ) + π ^{2} L ^{4} arccos ^{2} ( \frac{2}{L} )}{129600} + \frac{90 π L ^{2} - π L ^{2} arccos ( \frac{2}{L} )}{45} + 16

= \frac{8100 π ^{2} L ^{4} - 180 π ^{2} L ^{4} arccos ( \frac{2}{L} ) + π ^{2} L ^{4} arccos ^{2} ( \frac{2}{L} )}{129600} + \frac{90 π L ^{2} - π L ^{2} arccos ( \frac{2}{L} )}{45} + 16

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{8100 π ^{2} L ^{4} - 180 π ^{2} L ^{4} arccos ( \frac{2}{L} ) + π ^{2} L ^{4} arccos ^{2} ( \frac{2}{L} )}{129600} = \frac{8100 π ^{2} L ^{4}}{129600} - \frac{180 π ^{2} L ^{4} arccos ( \frac{2}{L} )}{129600} + \frac{π ^{2} L ^{4} arccos ^{2} ( \frac{2}{L} )}{129600}

= \frac{8100 π ^{2} L ^{4}}{129600} - \frac{180 π ^{2} L ^{4} arccos ( \frac{2}{L} )}{129600} + \frac{π ^{2} L ^{4} arccos ^{2} ( \frac{2}{L} )}{129600} + \frac{90 π L ^{2} - π L ^{2} arccos ( \frac{2}{L} )}{45} + 16

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{90 π L ^{2} - π L ^{2} arccos ( \frac{2}{L} )}{45} = \frac{90 π L ^{2}}{45} - \frac{π L ^{2} arccos ( \frac{2}{L} )}{45}

= \frac{8100 π ^{2} L ^{4}}{129600} - \frac{180 π ^{2} L ^{4} arccos ( \frac{2}{L} )}{129600} + \frac{π ^{2} L ^{4} arccos ^{2} ( \frac{2}{L} )}{129600} + \frac{90 π L ^{2}}{45} - \frac{π L ^{2} arccos ( \frac{2}{L} )}{45} + 16

Cancel

\frac{8100 π ^{2} L ^{4}}{129600} : \frac{π ^{2} L ^{4}}{16}

= \frac{π ^{2} L ^{4}}{16} - \frac{180 π ^{2} L ^{4} arccos ( \frac{2}{L} )}{129600} + \frac{π ^{2} L ^{4} arccos ^{2} ( \frac{2}{L} )}{129600} + \frac{90 π L ^{2}}{45} - \frac{π L ^{2} arccos ( \frac{2}{L} )}{45} + 16

Cancel

\frac{180 π ^{2} L ^{4} arccos ( \frac{2}{L} )}{129600} : \frac{π ^{2} L ^{4} arccos ( \frac{2}{L} )}{720}

= \frac{π ^{2} L ^{4}}{16} - \frac{π ^{2} L ^{4} arccos ( \frac{2}{L} )}{720} + \frac{π ^{2} L ^{4} arccos ^{2} ( \frac{2}{L} )}{129600} + \frac{90 π L ^{2}}{45} - \frac{π L ^{2} arccos ( \frac{2}{L} )}{45} + 16

Divide the numbers:

\frac{90}{45} = 2

= \frac{π ^{2} L ^{4}}{16} - \frac{π ^{2} L ^{4} arccos ( \frac{2}{L} )}{720} + \frac{π ^{2} L ^{4} arccos ^{2} ( \frac{2}{L} )}{129600} + 2 π L^{2} - \frac{π L ^{2} arccos ( \frac{2}{L} )}{45} + 16

(x + \frac{5}{x})^{9}

- 5 (2 + 3)

(x - \frac{1}{y ^{2}})^{12}

sin (x) (2 \cdot cos (x) - 1)

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

What is expand (-(piL^2(90-arccos(2/L)))/(360)-4)^2 ?
The solution to expand (-(piL^2(90-arccos(2/L)))/(360)-4)^2 is