What is expand (e^x+1)((e^{2x})/(4(e^x+1))+1) ?

The solution to expand (e^x+1)((e^{2x})/(4(e^x+1))+1) is (e^{2x})/4+e^x+1

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expand (e^x+1)((e^{2x})/(4(e^x+1))+1)

expand

(e^{x} + 1) (\frac{e ^{2 x}}{4 ( e ^{x} + 1 )} + 1)

\frac{e ^{2 x}}{4} + e^{x} + 1

Solution steps

(e^{x} + 1) (\frac{e ^{2 x}}{4 ( e ^{x} + 1 )} + 1)

Apply FOIL method:

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

a = e^{x}, b = 1, c = \frac{e ^{2 x}}{4 ( e ^{x} + 1 )}, d = 1

= e^{x} \frac{e ^{2 x}}{4 ( e ^{x} + 1 )} + e^{x} \cdot 1 + 1 \cdot \frac{e ^{2 x}}{4 ( e ^{x} + 1 )} + 1 \cdot 1

= e^{x} \frac{e ^{2 x}}{4 ( e ^{x} + 1 )} + 1 \cdot e^{x} + 1 \cdot \frac{e ^{2 x}}{4 ( e ^{x} + 1 )} + 1 \cdot 1

Simplify

e^{x} \frac{e ^{2 x}}{4 ( e ^{x} + 1 )} + 1 \cdot e^{x} + 1 \cdot \frac{e ^{2 x}}{4 ( e ^{x} + 1 )} + 1 \cdot 1 : \frac{e ^{2 x}}{4} + e^{x} + 1

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

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(7 - 3 y^{2} y + y^{2})^{2}

What is expand (e^x+1)((e^{2x})/(4(e^x+1))+1) ?
The solution to expand (e^x+1)((e^{2x})/(4(e^x+1))+1) is (e^{2x})/4+e^x+1