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

The solution to expand (1+e^{2x})^4(2) is 2+8e^{2x}+12e^{4x}+8e^{6x}+2e^{8x}

Popular >

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

expand

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

2 + 8 e^{2 x} + 12 e^{4 x} + 8 e^{6 x} + 2 e^{8 x}

Solution steps

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

Remove parentheses:

(a) = a

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

(1 + e^{2 x})^{4} = 1 + 4 e^{2 x} + 6 e^{4 x} + 4 e^{6 x} + e^{8 x}

= 2 (4 e^{2 x} + 6 e^{4 x} + 4 e^{6 x} + e^{8 x} + 1)

= 2 (1 + 4 e^{2 x} + 6 e^{4 x} + 4 e^{6 x} + e^{8 x})

Distribute parentheses

= 2 \cdot 1 + 2 \cdot 4 e^{2 x} + 2 \cdot 6 e^{4 x} + 2 \cdot 4 e^{6 x} + 2 e^{8 x}

Simplify

2 \cdot 1 + 2 \cdot 4 e^{2 x} + 2 \cdot 6 e^{4 x} + 2 \cdot 4 e^{6 x} + 2 e^{8 x} : 2 + 8 e^{2 x} + 12 e^{4 x} + 8 e^{6 x} + 2 e^{8 x}

= 2 + 8 e^{2 x} + 12 e^{4 x} + 8 e^{6 x} + 2 e^{8 x}

\frac{( 2 x - 1 ) ( 4 x ^{2} + 2 x + 1 )}{8}

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

\frac{b ^{2} ( 4 a ^{3} b ^{2} - 3 )}{a}

\frac{y ( y + x )}{y - x}

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

What is expand (1+e^{2x})^4(2) ?
The solution to expand (1+e^{2x})^4(2) is 2+8e^{2x}+12e^{4x}+8e^{6x}+2e^{8x}