What is expand (4x-1/2)^5 ?

The solution to expand (4x-1/2)^5 is 1024x^5-640x^4+160x^3-20x^2+(5x)/4-1/32

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expand (4x-1/2)^5

expand

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

1024 x^{5} - 640 x^{4} + 160 x^{3} - 20 x^{2} + \frac{5 x}{4} - \frac{1}{32}

Solution steps

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

Apply binomial theorem:

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

a = 4 x, b = - \frac{1}{2}

= i = 0 \sum 5 (i 5) (4 x)^{(5 - i)} (- \frac{1}{2})^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (4 x)^{5} (- \frac{1}{2})^{0} : 1024 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (4 x)^{4} (- \frac{1}{2})^{1} : - 640 x^{4}

Simplify

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

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (4 x)^{2} (- \frac{1}{2})^{3} : - 20 x^{2}

Simplify

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

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (4 x)^{0} (- \frac{1}{2})^{5} : - \frac{1}{32}

= 1024 x^{5} - 640 x^{4} + 160 x^{3} - 20 x^{2} + \frac{5 x}{4} - \frac{1}{32}

\frac{2}{7} + 3

2 + \frac{1}{12}

54 \cdot 34

(- 3 i) (4 i)

3. 3^{3}

What is expand (4x-1/2)^5 ?
The solution to expand (4x-1/2)^5 is 1024x^5-640x^4+160x^3-20x^2+(5x)/4-1/32