What is expand (2e^t+3t)^2 ?

The solution to expand (2e^t+3t)^2 is 4e^{2t}+12e^tt+9t^2

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expand (2e^t+3t)^2

expand

(2 e^{t} + 3 t)^{2}

4 e^{2 t} + 12 e^{t} t + 9 t^{2}

Solution steps

(2 e^{t} + 3 t)^{2}

Apply Perfect Square Formula:

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

a = 2 e^{t}, b = 3 t

= (2 e^{t})^{2} + 2 \cdot 2 e^{t} \cdot 3 t + (3 t)^{2}

Simplify

(2 e^{t})^{2} + 2 \cdot 2 e^{t} \cdot 3 t + (3 t)^{2} : 4 e^{2 t} + 12 e^{t} t + 9 t^{2}

= 4 e^{2 t} + 12 e^{t} t + 9 t^{2}

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

(x + 1) \times ln^{2} (x + 1)

sec (2 (arcsec (\frac{25}{7}) + 2 πn))

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

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

What is expand (2e^t+3t)^2 ?
The solution to expand (2e^t+3t)^2 is 4e^{2t}+12e^tt+9t^2