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

The solution to expand (4x-1)^4 is 256x^4-256x^3+96x^2-16x+1

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expand (4x-1)^4

expand

(4 x - 1)^{4}

256 x^{4} - 256 x^{3} + 96 x^{2} - 16 x + 1

Solution steps

(4 x - 1)^{4}

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 4 (i 4) (4 x)^{(4 - i)} (- 1)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (4 x)^{4} (- 1)^{0} : 256 x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (4 x)^{3} (- 1)^{1} : - 256 x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (4 x)^{2} (- 1)^{2} : 96 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (4 x)^{1} (- 1)^{3} : - 16 x

Simplify

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

= 256 x^{4} - 256 x^{3} + 96 x^{2} - 16 x + 1

27 x^{6} - 8

(2 + i) (3 + 2 i)

6 (4 y + 7 z)

(8 b + 9) - (7 b - 5)

8 x^{3} + 8

What is expand (4x-1)^4 ?
The solution to expand (4x-1)^4 is 256x^4-256x^3+96x^2-16x+1