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Popular >

expand (t-2)^4

Solution

expand

(t - 2)^{4}

Solution

t^{4} - 8 t^{3} + 24 t^{2} - 32 t + 16

Solution steps

(t - 2)^{4}

Apply binomial theorem:

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

a = t, b = - 2

= i = 0 \sum 4 (i 4) t^{(4 - i)} (- 2)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} t^{4} (- 2)^{0} : t^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} t^{3} (- 2)^{1} : - 8 t^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} t^{2} (- 2)^{2} : 24 t^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} t^{1} (- 2)^{3} : - 32 t

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} t^{0} (- 2)^{4} : 16

= t^{4} - 8 t^{3} + 24 t^{2} - 32 t + 16

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Frequently Asked Questions (FAQ)

What is expand (t-2)^4 ?
The solution to expand (t-2)^4 is t^4-8t^3+24t^2-32t+16