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

The solution to expand (4x-1)^5 is 1024x^5-1280x^4+640x^3-160x^2+20x-1

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expand (4x-1)^5

expand

(4 x - 1)^{5}

1024 x^{5} - 1280 x^{4} + 640 x^{3} - 160 x^{2} + 20 x - 1

Solution steps

(4 x - 1)^{5}

Apply binomial theorem:

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

a = 4 x, b = - 1

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

Expand summation

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

Simplify

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

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (4 x)^{4} (- 1)^{1} : - 1280 x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (4 x)^{3} (- 1)^{2} : 640 x^{3}

Simplify

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

Simplify

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

Simplify

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

= 1024 x^{5} - 1280 x^{4} + 640 x^{3} - 160 x^{2} + 20 x - 1

- 2 x^{3} (x - 1) (x + 5)

7 (\frac{x + 7}{5}) - 5

\frac{2}{3} \times \frac{4}{9}

\frac{38 - 20}{20}

What is expand (4x-1)^5 ?
The solution to expand (4x-1)^5 is 1024x^5-1280x^4+640x^3-160x^2+20x-1