What is (10-1/2 e^x)*(10-1/2 e^x) ?

The solution to (10-1/2 e^x)*(10-1/2 e^x) is -10e^x+1/4 e^{2x}+100

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simplify (10-1/2 e^x)*(10-1/2 e^x)

simplify

(10 - \frac{1}{2} e^{x}) \cdot (10 - \frac{1}{2} e^{x})

- 10 e^{x} + \frac{1}{4} e^{2 x} + 100

Solution steps

(10 - \frac{1}{2} e^{x}) (10 - \frac{1}{2} e^{x})

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

(10 - \frac{1}{2} e^{x}) (10 - \frac{1}{2} e^{x}) = (10 - \frac{1}{2} e^{x})^{1 + 1}

= (10 - \frac{1}{2} e^{x})^{1 + 1}

Add the numbers:

1 + 1 = 2

= (10 - \frac{1}{2} e^{x})^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = 10, b = \frac{1}{2} e^{x}

= 1 0^{2} - 2 \cdot 10 \cdot \frac{1}{2} e^{x} + (\frac{1}{2} e^{x})^{2}

Simplify

1 0^{2} - 2 \cdot 10 \cdot \frac{1}{2} e^{x} + (\frac{1}{2} e^{x})^{2} : 100 - 10 e^{x} + \frac{1}{4} e^{2 x}

= 100 - 10 e^{x} + \frac{1}{4} e^{2 x}

= - 10 e^{x} + \frac{1}{4} e^{2 x} + 100

- lo g_{10} (3.2) 1 0^{- 4}

2.3 \cdot 1 0^{- 5} e^{(- \frac{148000}{8.314 \cdot 900})}

10.2 \cdot 1 0^{- 3}

- 4 \cdot 8.314 \cdot 1 0^{- 3} \cdot 298.15

\frac{7}{3 y}

What is (10-1/2 e^x)*(10-1/2 e^x) ?
The solution to (10-1/2 e^x)*(10-1/2 e^x) is -10e^x+1/4 e^{2x}+100