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

The solution to expand (2x+5)^5 is 32x^5+400x^4+2000x^3+5000x^2+6250x+3125

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expand (2x+5)^5

expand

(2 x + 5)^{5}

32 x^{5} + 400 x^{4} + 2000 x^{3} + 5000 x^{2} + 6250 x + 3125

Solution steps

(2 x + 5)^{5}

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 5 (i 5) (2 x)^{(5 - i)} \cdot 5^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (2 x)^{5} \cdot 5^{0} : 32 x^{5}

Simplify

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

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (2 x)^{3} \cdot 5^{2} : 2000 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (2 x)^{2} \cdot 5^{3} : 5000 x^{2}

Simplify

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

Simplify

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

= 32 x^{5} + 400 x^{4} + 2000 x^{3} + 5000 x^{2} + 6250 x + 3125

\frac{4 x ^{2} - 12 x}{2 x ^{3} - 2 x ^{2} - 12 x}

(k + 3)^{3}

12 - (- 3)

\frac{200}{6}

(3 + 7)^{2}

What is expand (2x+5)^5 ?
The solution to expand (2x+5)^5 is 32x^5+400x^4+2000x^3+5000x^2+6250x+3125