What is expand 1/2 ((9-a^2)/2+1/2 (1/(e^6)-e^{-2a})) ?

The solution to expand 1/2 ((9-a^2)/2+1/2 (1/(e^6)-e^{-2a})) is -1/4 e^{-2a}+9/4+1/(4e^6)-(a^2)/4

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expand 1/2 ((9-a^2)/2+1/2 (1/(e^6)-e^{-2a}))

expand

\frac{1}{2} (\frac{9 - a ^{2}}{2} + \frac{1}{2} (\frac{1}{e ^{6}} - e^{- 2 a}))

- \frac{1}{4} e^{- 2 a} + \frac{9}{4} + \frac{1}{4 e ^{6}} - \frac{a ^{2}}{4}

Solution steps

\frac{1}{2} (\frac{9 - a ^{2}}{2} + \frac{1}{2} (\frac{1}{e ^{6}} - e^{- 2 a}))

Apply the distributive law:

a (b + c) = ab + a c

a = \frac{1}{2}, b = \frac{9 - a ^{2}}{2}, c = \frac{1}{2} (\frac{1}{e ^{6}} - e^{- 2 a})

= \frac{1}{2} \cdot \frac{9 - a ^{2}}{2} + \frac{1}{2} \cdot \frac{1}{2} (\frac{1}{e ^{6}} - e^{- 2 a})

Simplify

\frac{1}{2} \cdot \frac{9 - a ^{2}}{2} + \frac{1}{2} \cdot \frac{1}{2} (\frac{1}{e ^{6}} - e^{- 2 a}) : - \frac{1}{4} e^{- 2 a} + \frac{9}{4} + \frac{1}{4 e ^{6}} - \frac{a ^{2}}{4}

= - \frac{1}{4} e^{- 2 a} + \frac{9}{4} + \frac{1}{4 e ^{6}} - \frac{a ^{2}}{4}

(x^{2} + 1) sec (h) (ln (x))

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\frac{c ( b + 4 )}{( c + d )}

5 (2.5)^{3} - 3 (2.5)^{2} - 6 (2.5) - 16

What is expand 1/2 ((9-a^2)/2+1/2 (1/(e^6)-e^{-2a})) ?
The solution to expand 1/2 ((9-a^2)/2+1/2 (1/(e^6)-e^{-2a})) is -1/4 e^{-2a}+9/4+1/(4e^6)-(a^2)/4