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

The solution to expand (2+x)^4(1+1/(x^2)) is 16+32x+24x^2+8x^3+x^4+((2+x)^4)/(x^2)

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

expand

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

16 + 32 x + 24 x^{2} + 8 x^{3} + x^{4} + \frac{( 2 + x ) ^{4}}{x ^{2}}

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

Simplify

(2 + x)^{4} \cdot 1 + (2 + x)^{4} \frac{1}{x ^{2}} : 16 + 32 x + 24 x^{2} + 8 x^{3} + x^{4} + \frac{( 2 + x ) ^{4}}{x ^{2}}

= 16 + 32 x + 24 x^{2} + 8 x^{3} + x^{4} + \frac{( 2 + x ) ^{4}}{x ^{2}}

\frac{2 ( 1 - cos ( t ) )}{t}

(2 x + 3)^{2}

(1 - i)^{9}

(2 - 2 i)^{5}

(3 + 3 sin (x))^{2}

What is expand (2+x)^4(1+1/(x^2)) ?
The solution to expand (2+x)^4(1+1/(x^2)) is 16+32x+24x^2+8x^3+x^4+((2+x)^4)/(x^2)