What is expand (3e^{5t}-3e^{4t})(15e^{5t}-12e^{4t}) ?

The solution to expand (3e^{5t}-3e^{4t})(15e^{5t}-12e^{4t}) is 45e^{10t}-81e^{9t}+36e^{8t}

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expand (3e^{5t}-3e^{4t})(15e^{5t}-12e^{4t})

expand

(3 e^{5 t} - 3 e^{4 t}) (15 e^{5 t} - 12 e^{4 t})

45 e^{10 t} - 81 e^{9 t} + 36 e^{8 t}

Solution steps

(3 e^{5 t} - 3 e^{4 t}) (15 e^{5 t} - 12 e^{4 t})

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = 3 e^{5 t}, b = - 3 e^{4 t}, c = 15 e^{5 t}, d = - 12 e^{4 t}

= 3 e^{5 t} \cdot 15 e^{5 t} + 3 e^{5 t} (- 12 e^{4 t}) + (- 3 e^{4 t}) \cdot 15 e^{5 t} + (- 3 e^{4 t}) (- 12 e^{4 t})

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= 3 \cdot 15 e^{5 t} e^{5 t} - 3 \cdot 12 e^{5 t} e^{4 t} - 3 \cdot 15 e^{4 t} e^{5 t} + 3 \cdot 12 e^{4 t} e^{4 t}

Simplify

3 \cdot 15 e^{5 t} e^{5 t} - 3 \cdot 12 e^{5 t} e^{4 t} - 3 \cdot 15 e^{4 t} e^{5 t} + 3 \cdot 12 e^{4 t} e^{4 t} : 45 e^{10 t} - 81 e^{9 t} + 36 e^{8 t}

= 45 e^{10 t} - 81 e^{9 t} + 36 e^{8 t}

3 sec (\frac{π}{4} (x + 1))

ln (cos^{2} (t) + 1) \cdot ((e^{x^{2}} \cdot 2 x) i + sinh (t) j)

e^{2 x} (x^{3} + 5)

\frac{4 x + 6}{x ( x + 2 )}

2 t (45 cos (3 t) + 16 e^{- 4 t} - 8 sin (2 t))

What is expand (3e^{5t}-3e^{4t})(15e^{5t}-12e^{4t}) ?
The solution to expand (3e^{5t}-3e^{4t})(15e^{5t}-12e^{4t}) is 45e^{10t}-81e^{9t}+36e^{8t}