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Popular >

expand (1-sqrt(5))^5

Solution

expand

(1 - 5)^{5}

Solution

176 - 805

+1

Decimal Notation

- 2.88543 \dots

Solution steps

(1 - 5)^{5}

Apply binomial theorem:

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

a = 1, b = - 5

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

Expand summation

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

Simplify

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

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 1^{4} (- 5)^{1} : - 55

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 1^{3} (- 5)^{2} : 50

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 1^{2} (- 5)^{3} : - 505

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 1^{1} (- 5)^{4} : 125

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 1^{0} (- 5)^{5} : - 255

= 1 - 55 + 50 - 505 + 125 - 255

1 - 55 + 50 - 505 + 125 - 255 = 176 - 805

= 176 - 805

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Frequently Asked Questions (FAQ)

What is expand (1-sqrt(5))^5 ?
The solution to expand (1-sqrt(5))^5 is 176-80sqrt(5)