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)} (- 5)^{i}

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

4^{- 1.5}

4 m - 3 + 2 m + 5

1.0 1^{12}

\frac{n ^{2}}{n}

\frac{2}{2} + \frac{4}{2}

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