What is expand (e^x+7)(5e^x-2) ?

The solution to expand (e^x+7)(5e^x-2) is 5e^{2x}+33e^x-14

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expand (e^x+7)(5e^x-2)

expand

(e^{x} + 7) (5 e^{x} - 2)

5 e^{2 x} + 33 e^{x} - 14

Solution steps

(e^{x} + 7) (5 e^{x} - 2)

Apply FOIL method:

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

a = e^{x}, b = 7, c = 5 e^{x}, d = - 2

= e^{x} \cdot 5 e^{x} + e^{x} (- 2) + 7 \cdot 5 e^{x} + 7 (- 2)

Apply minus-plus rules

+ (- a) = - a

= 5 e^{x} e^{x} - 2 e^{x} + 7 \cdot 5 e^{x} - 7 \cdot 2

Simplify

5 e^{x} e^{x} - 2 e^{x} + 7 \cdot 5 e^{x} - 7 \cdot 2 : 5 e^{2 x} + 33 e^{x} - 14

= 5 e^{2 x} + 33 e^{x} - 14

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What is expand (e^x+7)(5e^x-2) ?
The solution to expand (e^x+7)(5e^x-2) is 5e^{2x}+33e^x-14