What is expand (sqrt(x)+3)^4 ?

The solution to expand (sqrt(x)+3)^4 is x^2+12xsqrt(x)+54x+108sqrt(x)+81

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expand (sqrt(x)+3)^4

expand

(x + 3)^{4}

x^{2} + 12 x x + 54 x + 108 x + 81

Solution steps

(x + 3)^{4}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = x, b = 3

= i = 0 \sum 4 (i 4) (x)^{(4 - i)} \cdot 3^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (x)^{4} \cdot 3^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (x)^{3} \cdot 3^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (x)^{2} \cdot 3^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (x)^{1} \cdot 3^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (x)^{0} \cdot 3^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (x)^{4} \cdot 3^{0} : x^{2}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x)^{3} \cdot 3^{1} : 12 (x)^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (x)^{2} \cdot 3^{2} : 54 x

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (x)^{1} \cdot 3^{3} : 108 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (x)^{0} \cdot 3^{4} : 81

= x^{2} + 12 (x)^{3} + 54 x + 108 x + 81

Simplify

(x)^{3} : x x

= x^{2} + 12 x x + 54 x + 108 x + 81

(x - \frac{2}{x})^{5}

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

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

(x + 37) (x - 7)

\frac{1}{( 1 - i 3 ) ^{4}}

What is expand (sqrt(x)+3)^4 ?
The solution to expand (sqrt(x)+3)^4 is x^2+12xsqrt(x)+54x+108sqrt(x)+81