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}

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

22 (- 2 + 1)

\frac{( 4 x + 4 )}{( 2 x - 4 )}

\frac{d ^{3}}{d y d x ^{2}} ((f (y, x)) (2 x^{3} + x^{2} y^{4} - 5 y^{2}))

\frac{3}{( 4 + 9 e ^{5 x} ) ^{4}}

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