What is expand (3+4sin(2000pit))^2 ?

The solution to expand (3+4sin(2000pit))^2 is 9+24sin(2000pit)+16sin^2(2000pit)

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expand (3+4sin(2000pit))^2

expand

(3 + 4 sin (2000 π t))^{2}

9 + 24 sin (2000 π t) + 16 sin^{2} (2000 π t)

Solution steps

(3 + 4 sin (2000 π t))^{2}

Apply Perfect Square Formula:

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

a = 3, b = 4 sin (2000 π t)

= 3^{2} + 2 \cdot 3 \cdot 4 sin (2000 π t) + (4 sin (2000 π t))^{2}

Simplify

3^{2} + 2 \cdot 3 \cdot 4 sin (2000 π t) + (4 sin (2000 π t))^{2} : 9 + 24 sin (2000 π t) + 16 sin^{2} (2000 π t)

= 9 + 24 sin (2000 π t) + 16 sin^{2} (2000 π t)

(1 - \frac{3}{4} x)^{8}

\frac{1}{( s + 4 ) ( s ^{2} + 1 )}

\frac{2 x ^{3} + 4 x ^{2} - 14 x}{( x - 4 ) ( x + 2 )}

\frac{\partial}{\partial y} ((u) (C y (2 h - y)))

What is expand (3+4sin(2000pit))^2 ?
The solution to expand (3+4sin(2000pit))^2 is 9+24sin(2000pit)+16sin^2(2000pit)