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

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

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expand (2x+5)^4

expand

(2 x + 5)^{4}

16 x^{4} + 160 x^{3} + 600 x^{2} + 1000 x + 625

Solution steps

(2 x + 5)^{4}

Apply binomial theorem:

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

a = 2 x, b = 5

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

= 16 x^{4} + 160 x^{3} + 600 x^{2} + 1000 x + 625

\frac{4 x}{x ^{2} - 4} \cdot \frac{x + 2}{16 x}

cot^{2} (x) (1 + tan^{2} (x))

(5 x - 2) (2 y - 5)

f (a) = \frac{2 a + 2}{a ^{2} - 1}

\frac{1 + i}{3 + i}

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