What is expand (a+sqrt(b))^4 ?

The solution to expand (a+sqrt(b))^4 is a^4+4a^3sqrt(b)+6a^2b+4absqrt(b)+b^2

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expand (a+sqrt(b))^4

expand

(a + b)^{4}

a^{4} + 4 a^{3} b + 6 a^{2} b + 4 ab b + b^{2}

Solution steps

(a + b)^{4}

Apply binomial theorem:

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

a = a, b = b

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

Simplify

(b)^{3} : b b

= a^{4} + 4 a^{3} b + 6 a^{2} b + 4 ab b + b^{2}

(1 - x^{2}) d x

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5 (2 x + 4 - x + 10 = 3 x + 3)

(x y^{2} + x) d y

What is expand (a+sqrt(b))^4 ?
The solution to expand (a+sqrt(b))^4 is a^4+4a^3sqrt(b)+6a^2b+4absqrt(b)+b^2