What is expand (sqrt(a)-sqrt(x))^4 ?

The solution to expand (sqrt(a)-sqrt(x))^4 is a^2-4sqrt(x)asqrt(a)+6ax-4sqrt(a)xsqrt(x)+x^2

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expand (sqrt(a)-sqrt(x))^4

expand

(a - x)^{4}

a^{2} - 4 x a a + 6 a x - 4 a x x + x^{2}

Solution steps

(a - x)^{4}

Apply binomial theorem:

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

a = a, b = - x

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

(a)^{3} = a a

(x)^{3} = x x

= a^{2} - 4 x a a + 6 a x - 4 a x x + x^{2}

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

25 (6 + 2)

(6 + 8 i)^{8}

(1 + i)^{5} + (1 - i)^{5}

(1 + e^{2 x})^{2}

What is expand (sqrt(a)-sqrt(x))^4 ?
The solution to expand (sqrt(a)-sqrt(x))^4 is a^2-4sqrt(x)asqrt(a)+6ax-4sqrt(a)xsqrt(x)+x^2