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Popular >

expand (x-1)^5

Solution

expand

(x - 1)^{5}

Solution

x^{5} - 5 x^{4} + 10 x^{3} - 10 x^{2} + 5 x - 1

Solution steps

(x - 1)^{5}

Apply binomial theorem:

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

a = x, b = - 1

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} (- 1)^{2} : 10 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} (- 1)^{3} : - 10 x^{2}

Simplify

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

Simplify

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

= x^{5} - 5 x^{4} + 10 x^{3} - 10 x^{2} + 5 x - 1

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Frequently Asked Questions (FAQ)

What is expand (x-1)^5 ?
The solution to expand (x-1)^5 is x^5-5x^4+10x^3-10x^2+5x-1