What is expand (sqrt(x)+6)^4 ?

The solution to expand (sqrt(x)+6)^4 is x^2+24xsqrt(x)+216x+864sqrt(x)+1296

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expand (sqrt(x)+6)^4

expand

(x + 6)^{4}

x^{2} + 24 x x + 216 x + 864 x + 1296

Solution steps

(x + 6)^{4}

Apply binomial theorem:

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

a = x, b = 6

= i = 0 \sum 4 (i 4) (x)^{(4 - i)} \cdot 6^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (x)^{4} \cdot 6^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (x)^{3} \cdot 6^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (x)^{2} \cdot 6^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (x)^{1} \cdot 6^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (x)^{0} \cdot 6^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (x)^{4} \cdot 6^{0} : x^{2}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x)^{3} \cdot 6^{1} : 24 (x)^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (x)^{2} \cdot 6^{2} : 216 x

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (x)^{1} \cdot 6^{3} : 864 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (x)^{0} \cdot 6^{4} : 1296

= x^{2} + 24 (x)^{3} + 216 x + 864 x + 1296

Simplify

(x)^{3} : x x

= x^{2} + 24 x x + 216 x + 864 x + 1296

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

\frac{( 5 s ^{2} - 14 s + 8 )}{( s ( s - 1 ) ( s - 3 ) )}

\frac{( x - 2 ) ( 3 x - y )}{x ^{2} ( x - 7 )}

(1 + X)^{4}

x^{2} + x + 4 \cdot (3 x^{2} - 4 x)

What is expand (sqrt(x)+6)^4 ?
The solution to expand (sqrt(x)+6)^4 is x^2+24xsqrt(x)+216x+864sqrt(x)+1296