What is expand (3e^{5t}-2e^{4t})(15e^{5t}-8e^{4t}) ?

The solution to expand (3e^{5t}-2e^{4t})(15e^{5t}-8e^{4t}) is 45e^{10t}-54e^{9t}+16e^{8t}

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expand (3e^{5t}-2e^{4t})(15e^{5t}-8e^{4t})

expand

(3 e^{5 t} - 2 e^{4 t}) (15 e^{5 t} - 8 e^{4 t})

45 e^{10 t} - 54 e^{9 t} + 16 e^{8 t}

Solution steps

(3 e^{5 t} - 2 e^{4 t}) (15 e^{5 t} - 8 e^{4 t})

Apply FOIL method:

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

a = 3 e^{5 t}, b = - 2 e^{4 t}, c = 15 e^{5 t}, d = - 8 e^{4 t}

= 3 e^{5 t} \cdot 15 e^{5 t} + 3 e^{5 t} (- 8 e^{4 t}) + (- 2 e^{4 t}) \cdot 15 e^{5 t} + (- 2 e^{4 t}) (- 8 e^{4 t})

Apply minus-plus rules

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

= 3 \cdot 15 e^{5 t} e^{5 t} - 3 \cdot 8 e^{5 t} e^{4 t} - 2 \cdot 15 e^{4 t} e^{5 t} + 2 \cdot 8 e^{4 t} e^{4 t}

Simplify

3 \cdot 15 e^{5 t} e^{5 t} - 3 \cdot 8 e^{5 t} e^{4 t} - 2 \cdot 15 e^{4 t} e^{5 t} + 2 \cdot 8 e^{4 t} e^{4 t} : 45 e^{10 t} - 54 e^{9 t} + 16 e^{8 t}

= 45 e^{10 t} - 54 e^{9 t} + 16 e^{8 t}

\frac{x ^{2} ( - \frac{x}{2} + 4 ) ^{4}}{32}

\frac{f ( x + h ) - 8 x + 2}{h}

\frac{- e ^{t} t + 2 e ^{t}}{( 1 - t ) ^{2}}

- \frac{( 3 \cdot F \cdot ( a \cdot x ^{n} + α \cdot n - α ) )}{( 5 \cdot x ^{n} )}

\frac{15 s}{( s ^{2} + 25 ) ^{2}}

What is expand (3e^{5t}-2e^{4t})(15e^{5t}-8e^{4t}) ?
The solution to expand (3e^{5t}-2e^{4t})(15e^{5t}-8e^{4t}) is 45e^{10t}-54e^{9t}+16e^{8t}