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)} (- 5)^{i}

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{64 \cdot 2 \cdot ( \frac{1}{4} ) ^{2}}{2 \frac{3}{2}}

\frac{csc ( x ) sin ( x )}{cot ( x )}

\frac{3}{32} - (- \frac{1}{48})

[\frac{2 x ^{- 2} y ^{2} \cdot ( - x ^{2} )}{( 2 y ^{4} ) ^{4}}]^{4}

\frac{( 5 ^{2} ) ^{3}}{( 5 ^{3} ) ^{7}}

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