What is expand (2t-3)e^{(t+3)/2} ?

The solution to expand (2t-3)e^{(t+3)/2} is 2e^{(t+3)/2}t-3e^{(t+3)/2}

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expand (2t-3)e^{(t+3)/2}

expand

(2 t - 3) e^{\frac{t + 3}{2}}

2 e^{\frac{t + 3}{2}} t - 3 e^{\frac{t + 3}{2}}

Solution steps

(2 t - 3) e^{\frac{t + 3}{2}}

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

Apply the distributive law:

a (b - c) = ab - a c

a = e^{\frac{t + 3}{2}}, b = 2 t, c = 3

= e^{\frac{t + 3}{2}} \cdot 2 t - e^{\frac{t + 3}{2}} \cdot 3

= 2 e^{\frac{t + 3}{2}} t - 3 e^{\frac{t + 3}{2}}

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What is expand (2t-3)e^{(t+3)/2} ?
The solution to expand (2t-3)e^{(t+3)/2} is 2e^{(t+3)/2}t-3e^{(t+3)/2}