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

The solution to expand ((x+1)^4)/2 is (x^4)/2+2x^3+3x^2+2x+1/2

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expand ((x+1)^4)/2

expand

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

\frac{x ^{4}}{2} + 2 x^{3} + 3 x^{2} + 2 x + \frac{1}{2}

Solution steps

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

(x + 1)^{4} = x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 1

= \frac{x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1}{2}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1}{2} = \frac{x ^{4}}{2} + \frac{4 x ^{3}}{2} + \frac{6 x ^{2}}{2} + \frac{4 x}{2} + \frac{1}{2}

= \frac{x ^{4}}{2} + \frac{4 x ^{3}}{2} + \frac{6 x ^{2}}{2} + \frac{4 x}{2} + \frac{1}{2}

Divide the numbers:

\frac{4}{2} = 2

= \frac{x ^{4}}{2} + 2 x^{3} + \frac{6 x ^{2}}{2} + \frac{4 x}{2} + \frac{1}{2}

Divide the numbers:

\frac{6}{2} = 3

= \frac{x ^{4}}{2} + 2 x^{3} + 3 x^{2} + \frac{4 x}{2} + \frac{1}{2}

Divide the numbers:

\frac{4}{2} = 2

= \frac{x ^{4}}{2} + 2 x^{3} + 3 x^{2} + 2 x + \frac{1}{2}

\frac{3 x ( x - 5 )}{( x + 2 ) ( x + 1 )}

(e^{5 m} - f^{n})^{2}

\frac{2 + 3 x}{( x + 4 ) ( x ^{2} - 5 x + 6 )}

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

\frac{1}{2 ( x + h )}

What is expand ((x+1)^4)/2 ?
The solution to expand ((x+1)^4)/2 is (x^4)/2+2x^3+3x^2+2x+1/2