What is expand (x^2+4)^5 ?

The solution to expand (x^2+4)^5 is x^{10}+20x^8+160x^6+640x^4+1280x^2+1024

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expand (x^2+4)^5

expand

(x^{2} + 4)^{5}

x^{10} + 20 x^{8} + 160 x^{6} + 640 x^{4} + 1280 x^{2} + 1024

Solution steps

(x^{2} + 4)^{5}

Apply binomial theorem:

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

a = x^{2}, b = 4

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

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (x^{2})^{5} \cdot 4^{0} : x^{10}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (x^{2})^{4} \cdot 4^{1} : 20 x^{8}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (x^{2})^{3} \cdot 4^{2} : 160 x^{6}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (x^{2})^{2} \cdot 4^{3} : 640 x^{4}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (x^{2})^{1} \cdot 4^{4} : 1280 x^{2}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (x^{2})^{0} \cdot 4^{5} : 1024

= x^{10} + 20 x^{8} + 160 x^{6} + 640 x^{4} + 1280 x^{2} + 1024

\int (e^{2 x}) d x

x^{x}

\frac{d}{d x} (\frac{1}{10 x + 11})

\int_{- \infty}^{0} \frac{1}{x ^{2} + 1} d x

\frac{\partial}{\partial y} (4 arctan (\frac{x}{y}))

What is expand (x^2+4)^5 ?
The solution to expand (x^2+4)^5 is x^{10}+20x^8+160x^6+640x^4+1280x^2+1024