What is expand (1+2pi*sin(2pix))^2 ?

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

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expand (1+2pi*sin(2pix))^2

expand

(1 + 2 π \cdot sin (2 π x))^{2}

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

Solution steps

(1 + 2 π sin (2 π x))^{2}

Apply Perfect Square Formula:

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

a = 1, b = 2 π sin (2 π x)

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

Simplify

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

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

\frac{7}{( s ^{2} + 49 ) ( s ^{2} + 9 )}

(4 x - 2 y) d x

(y - x) d x

(t - e^{i θ}) (t - 2)

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

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