What is expand (5+2x^{1/2})^4 ?

The solution to expand (5+2x^{1/2})^4 is 625+1000x^{1/2}+600x+160x^{3/2}+16x^2

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expand (5+2x^{1/2})^4

expand

(5 + 2 x^{\frac{1}{2}})^{4}

625 + 1000 x^{\frac{1}{2}} + 600 x + 160 x^{\frac{3}{2}} + 16 x^{2}

Solution steps

(5 + 2 x^{\frac{1}{2}})^{4}

Apply binomial theorem:

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

a = 5, b = 2 x^{\frac{1}{2}}

= i = 0 \sum 4 (i 4) \cdot 5^{(4 - i)} (2 x^{\frac{1}{2}})^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 5^{4} (2 x^{\frac{1}{2}})^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 5^{3} (2 x^{\frac{1}{2}})^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 5^{2} (2 x^{\frac{1}{2}})^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 5^{1} (2 x^{\frac{1}{2}})^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 5^{0} (2 x^{\frac{1}{2}})^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 5^{4} (2 x^{\frac{1}{2}})^{0} : 625

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 5^{3} (2 x^{\frac{1}{2}})^{1} : 1000 x^{\frac{1}{2}}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 5^{2} (2 x^{\frac{1}{2}})^{2} : 600 x

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 5^{1} (2 x^{\frac{1}{2}})^{3} : 160 x^{\frac{3}{2}}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 5^{0} (2 x^{\frac{1}{2}})^{4} : 16 x^{2}

= 625 + 1000 x^{\frac{1}{2}} + 600 x + 160 x^{\frac{3}{2}} + 16 x^{2}

(x + 2 - 3) \cdot (x + 2 + 3)

2 (2 + 3)

100.2 + \frac{28.9}{x ( 1 + x )}

\frac{1}{( 5 x + 1 ) ^{3}}

\frac{16}{( x - 2 ) ^{2}}

What is expand (5+2x^{1/2})^4 ?
The solution to expand (5+2x^{1/2})^4 is 625+1000x^{1/2}+600x+160x^{3/2}+16x^2