What is expand e^{3x}(e^{2x}-e^x) ?

The solution to expand e^{3x}(e^{2x}-e^x) is e^{5x}-e^{4x}

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expand e^{3x}(e^{2x}-e^x)

expand

e^{3 x} (e^{2 x} - e^{x})

e^{5 x} - e^{4 x}

Solution steps

e^{3 x} (e^{2 x} - e^{x})

Apply the distributive law:

a (b - c) = ab - a c

a = e^{3 x}, b = e^{2 x}, c = e^{x}

= e^{3 x} e^{2 x} - e^{3 x} e^{x}

= e^{3 x} e^{2 x} - e^{x} e^{3 x}

Simplify

e^{3 x} e^{2 x} - e^{x} e^{3 x} : e^{5 x} - e^{4 x}

= e^{5 x} - e^{4 x}

(e^{2 x} - 4) (e^{2 x} + 4)

(e^{3 x} + 6) (e^{3 x} - 4)

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

(x + Δ x)^{2} - 4 (x + Δ x)

\frac{( x + 2 ) ( x + 5 )}{( x + 6 ) ( x + 7 )}

What is expand e^{3x}(e^{2x}-e^x) ?
The solution to expand e^{3x}(e^{2x}-e^x) is e^{5x}-e^{4x}