What is expand (2pi*i*s+a)^2 ?

The solution to expand (2pi*i*s+a)^2 is (-4pi^2s^2+a^2)+4piias

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expand (2piis+a)^2

expand

(2 π \cdot i \cdot s + a)^{2}

(- 4 π^{2} s^{2} + a^{2}) + 4 πia s

Solution steps

(2 πi s + a)^{2}

Apply Perfect Square Formula:

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

a = 2 πi s, b = a

= (2 πi s)^{2} + 2 \cdot 2 πi s a + a^{2}

Simplify

(2 πi s)^{2} + 2 \cdot 2 πi s a + a^{2} : - 4 π^{2} s^{2} + 4 πia s + a^{2}

= - 4 π^{2} s^{2} + 4 πia s + a^{2}

Rewrite

- 4 π^{2} s^{2} + 4 πia s + a^{2}

in standard complex form:

(- 4 π^{2} s^{2} + a^{2}) + 4 πa s i

= (- 4 π^{2} s^{2} + a^{2}) + 4 πa s i

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

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

- \frac{24 x}{( x ^{2} + 3 ) ^{2}}

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

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

What is expand (2pi*i*s+a)^2 ?
The solution to expand (2pi*i*s+a)^2 is (-4pi^2s^2+a^2)+4piias