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Popular >

expand (t-1)^4

Solution

expand

(t - 1)^{4}

Solution

t^{4} - 4 t^{3} + 6 t^{2} - 4 t + 1

Solution steps

(t - 1)^{4}

Apply binomial theorem:

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

a = t, b = - 1

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} t^{2} (- 1)^{2} : 6 t^{2}

Simplify

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

Simplify

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

= t^{4} - 4 t^{3} + 6 t^{2} - 4 t + 1

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Frequently Asked Questions (FAQ)

What is expand (t-1)^4 ?
The solution to expand (t-1)^4 is t^4-4t^3+6t^2-4t+1