What is expand (1+2pisin(2pit))^2 ?

The solution to expand (1+2pisin(2pit))^2 is 1+4pisin(2pit)+4pi^2sin^2(2pit)

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expand (1+2pisin(2pit))^2

expand

(1 + 2 π sin (2 π t))^{2}

1 + 4 π sin (2 π t) + 4 π^{2} sin^{2} (2 π t)

Solution steps

(1 + 2 π sin (2 π t))^{2}

Apply Perfect Square Formula:

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

a = 1, b = 2 π sin (2 π t)

= 1^{2} + 2 \cdot 1 \cdot 2 π sin (2 π t) + (2 π sin (2 π t))^{2}

Simplify

1^{2} + 2 \cdot 1 \cdot 2 π sin (2 π t) + (2 π sin (2 π t))^{2} : 1 + 4 π sin (2 π t) + 4 π^{2} sin^{2} (2 π t)

= 1 + 4 π sin (2 π t) + 4 π^{2} sin^{2} (2 π t)

\frac{\partial}{\partial x} ((z) (x^{2} + y^{2} + x y))

\frac{( 1 + a ) ^{n} + 2}{( 1 + a ) ^{2 n}}

\frac{2 x + 11}{( x - 2 ) ( x + 3 )}

(w - \frac{3}{2}) (w + \frac{7}{2})

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

What is expand (1+2pisin(2pit))^2 ?
The solution to expand (1+2pisin(2pit))^2 is 1+4pisin(2pit)+4pi^2sin^2(2pit)