What is expand (6e^x-7)(e^x+5) ?

The solution to expand (6e^x-7)(e^x+5) is 6e^{2x}+23e^x-35

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expand (6e^x-7)(e^x+5)

expand

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

6 e^{2 x} + 23 e^{x} - 35

Solution steps

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

Apply FOIL method:

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

a = 6 e^{x}, b = - 7, c = e^{x}, d = 5

= 6 e^{x} e^{x} + 6 e^{x} \cdot 5 + (- 7) e^{x} + (- 7) \cdot 5

Apply minus-plus rules

+ (- a) = - a

= 6 e^{x} e^{x} + 6 \cdot 5 e^{x} - 7 e^{x} - 7 \cdot 5

Simplify

6 e^{x} e^{x} + 6 \cdot 5 e^{x} - 7 e^{x} - 7 \cdot 5 : 6 e^{2 x} + 23 e^{x} - 35

= 6 e^{2 x} + 23 e^{x} - 35

(7 + 8) \cdot (63)

(1 + i) (a - bi) (3 + i)

\frac{( x ^{2} - x ) ( x + 1 )}{x - 1}

(x - \frac{15}{4})^{2}

(2 + i) (1 + 2 i, 3 - i)

What is expand (6e^x-7)(e^x+5) ?
The solution to expand (6e^x-7)(e^x+5) is 6e^{2x}+23e^x-35