What is expand (2t-e^{4t})^2 ?

The solution to expand (2t-e^{4t})^2 is 4t^2-4e^{4t}t+e^{8t}

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expand (2t-e^{4t})^2

expand

(2 t - e^{4 t})^{2}

4 t^{2} - 4 e^{4 t} t + e^{8 t}

Solution steps

(2 t - e^{4 t})^{2}

Apply Perfect Square Formula:

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

a = 2 t, b = e^{4 t}

= (2 t)^{2} - 2 \cdot 2 t e^{4 t} + (e^{4 t})^{2}

Simplify

(2 t)^{2} - 2 \cdot 2 t e^{4 t} + (e^{4 t})^{2} : 4 t^{2} - 4 e^{4 t} t + e^{8 t}

= 4 t^{2} - 4 e^{4 t} t + e^{8 t}

(8 x + 7) (- e^{- x})

(- 1 + t)^{2} + (- 4 - 2 t)^{2} + (5 + 2 t)^{2}

\frac{5 ( 1 + 7 )}{3}

(x + h)^{2} + 1 - x^{2} + 1

\frac{x ( x ^{2} + 8 x + 2 )}{9}

What is expand (2t-e^{4t})^2 ?
The solution to expand (2t-e^{4t})^2 is 4t^2-4e^{4t}t+e^{8t}