What is expand (1+sqrt(x))^4 ?

The solution to expand (1+sqrt(x))^4 is 1+4sqrt(x)+6x+4xsqrt(x)+x^2

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expand (1+sqrt(x))^4

expand

(1 + x)^{4}

1 + 4 x + 6 x + 4 x x + x^{2}

Solution steps

(1 + x)^{4}

Apply binomial theorem:

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

a = 1, b = x

= i = 0 \sum 4 (i 4) \cdot 1^{(4 - i)} (x)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} (x)^{0} : 1

Simplify

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

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 1^{2} (x)^{2} : 6 x

Simplify

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

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (x)^{4} : x^{2}

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

Simplify

(x)^{3} : x x

= 1 + 4 x + 6 x + 4 x x + x^{2}

- \frac{7 x - 15}{( x - 1 ) ^{2}}

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

lo g_{10} (\frac{3 x}{4 x ^{2} - 9})

(sec (x) + tan (x)) cos (x) - sin (x)

\frac{1}{2} + \frac{1}{4} (0.9 - 1)

What is expand (1+sqrt(x))^4 ?
The solution to expand (1+sqrt(x))^4 is 1+4sqrt(x)+6x+4xsqrt(x)+x^2