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

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

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

expand

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

e^{3 x} + e^{2 x} + e^{x} + 1

Solution steps

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

Apply FOIL method:

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

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

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

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

Simplify

e^{x} e^{2 x} + 1 \cdot e^{2 x} + 1 \cdot e^{x} + 1 \cdot 1 : e^{3 x} + e^{2 x} + e^{x} + 1

= e^{3 x} + e^{2 x} + e^{x} + 1

\frac{( 2 x + 1 ) ( x + 4 ) ( x - 3 )}{( x - 2 ) ^{3} ( x + 3 ) ^{3}}

- \frac{2 a ( b ^{2} - 3 x ^{2} )}{( x ^{2} + b ^{2} ) ^{3}}

(x 3 - y)^{2}

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