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

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

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expand (4t-1)^4

expand

(4 t - 1)^{4}

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

Solution steps

(4 t - 1)^{4}

Apply binomial theorem:

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

a = 4 t, b = - 1

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{1}{4} x^{2} - 1

6 a^{2} - 19 a + 10

\frac{8 x}{4 x ^{2}}

3 + 16 x^{2} + 55 x - 72

- (\frac{220}{45.87 + 45})

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