What is expand (e^x-2e^{2x})(-6e^x+1) ?

The solution to expand (e^x-2e^{2x})(-6e^x+1) is e^x-8e^{2x}+12e^{3x}

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expand (e^x-2e^{2x})(-6e^x+1)

expand

(e^{x} - 2 e^{2 x}) (- 6 e^{x} + 1)

e^{x} - 8 e^{2 x} + 12 e^{3 x}

Solution steps

(e^{x} - 2 e^{2 x}) (- 6 e^{x} + 1)

Apply FOIL method:

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

a = e^{x}, b = - 2 e^{2 x}, c = - 6 e^{x}, d = 1

= e^{x} (- 6 e^{x}) + e^{x} \cdot 1 + (- 2 e^{2 x}) (- 6 e^{x}) + (- 2 e^{2 x}) \cdot 1

Apply minus-plus rules

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

= - 6 e^{x} e^{x} + 1 \cdot e^{x} + 2 \cdot 6 e^{x} e^{2 x} - 2 \cdot 1 \cdot e^{2 x}

Simplify

- 6 e^{x} e^{x} + 1 \cdot e^{x} + 2 \cdot 6 e^{x} e^{2 x} - 2 \cdot 1 \cdot e^{2 x} : e^{x} - 8 e^{2 x} + 12 e^{3 x}

= e^{x} - 8 e^{2 x} + 12 e^{3 x}

\frac{b}{( x + b + 1 ) ( x + 1 )}

5 (6 x + 7 + 4 = 29)

(3) + (3 - 3 x) d x

(x y + y^{2}) d x - (x^{2}) d y

(x + δ)^{2} - 9 (x + δ) - 6

What is expand (e^x-2e^{2x})(-6e^x+1) ?
The solution to expand (e^x-2e^{2x})(-6e^x+1) is e^x-8e^{2x}+12e^{3x}