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

The solution to expand (2s^4+5)^5 is 32s^{20}+400s^{16}+2000s^{12}+5000s^8+6250s^4+3125

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expand (2s^4+5)^5

expand

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

32 s^{20} + 400 s^{16} + 2000 s^{12} + 5000 s^{8} + 6250 s^{4} + 3125

Solution steps

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

Apply binomial theorem:

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

a = 2 s^{4}, b = 5

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

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (2 s^{4})^{5} \cdot 5^{0} : 32 s^{20}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (2 s^{4})^{4} \cdot 5^{1} : 400 s^{16}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (2 s^{4})^{3} \cdot 5^{2} : 2000 s^{12}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (2 s^{4})^{2} \cdot 5^{3} : 5000 s^{8}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (2 s^{4})^{1} \cdot 5^{4} : 6250 s^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (2 s^{4})^{0} \cdot 5^{5} : 3125

= 32 s^{20} + 400 s^{16} + 2000 s^{12} + 5000 s^{8} + 6250 s^{4} + 3125

(x^{n} y^{- m})^{4} \cdot (x^{3} y^{- 2})^{- n}

\frac{( sin ( 14 x ) + a \cdot sin ( x ) )}{( 10 x ^{3} )}

(x^{3} - 3 x^{2} - 4 x)^{0.5}

(\frac{a}{3} - \frac{b}{5}) (\frac{3}{a} - \frac{5}{b})

- 3 x^{2} - 16 x - 75

What is expand (2s^4+5)^5 ?
The solution to expand (2s^4+5)^5 is 32s^{20}+400s^{16}+2000s^{12}+5000s^8+6250s^4+3125