What is expand (1+2x)(1+x/2)^9 ?

The solution to expand (1+2x)(1+x/2)^9 is ((2+x)^9)/(512)+((2+x)^9x)/(256)

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expand (1+2x)(1+x/2)^9

expand

(1 + 2 x) (1 + \frac{x}{2})^{9}

\frac{( 2 + x ) ^{9}}{512} + \frac{( 2 + x ) ^{9} x}{256}

Solution steps

(1 + 2 x) (1 + \frac{x}{2})^{9}

= (1 + \frac{x}{2})^{9} (1 + 2 x)

Apply the distributive law:

a (b + c) = ab + a c

(1 + \frac{x}{2})^{9} (1 + 2 x) = (1 + \frac{x}{2})^{9} \cdot 1 + (1 + \frac{x}{2})^{9} \cdot 2 x

= (1 + \frac{x}{2})^{9} \cdot 1 + (1 + \frac{x}{2})^{9} \cdot 2 x

Simplify

(1 + \frac{x}{2})^{9} \cdot 1 + (1 + \frac{x}{2})^{9} \cdot 2 x : \frac{( 2 + x ) ^{9}}{512} + \frac{( 2 + x ) ^{9} x}{256}

= \frac{( 2 + x ) ^{9}}{512} + \frac{( 2 + x ) ^{9} x}{256}

\frac{1}{2} (x + \frac{1}{6} sin (6 x))

(5 x^{2} - 3 x - 1)^{6}

(x + 1 - 2) \cdot (x + 1 + 2)

6 (\frac{w}{2} - \frac{3}{4})

(a + b e + c e^{2} + d e^{3})^{3}

What is expand (1+2x)(1+x/2)^9 ?
The solution to expand (1+2x)(1+x/2)^9 is ((2+x)^9)/(512)+((2+x)^9x)/(256)