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Popular >

expand (sqrt(3)-1)^5

Solution

expand

(3 - 1)^{5}

Solution

443 - 76

+1

Decimal Notation

0.21023 \dots

Solution steps

(3 - 1)^{5}

Apply binomial theorem:

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

a = 3, b = - 1

= i = 0 \sum 5 (i 5) (3)^{(5 - i)} (- 1)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (3)^{5} (- 1)^{0} : 93

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (3)^{4} (- 1)^{1} : - 45

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (3)^{3} (- 1)^{2} : 303

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (3)^{2} (- 1)^{3} : - 30

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (3)^{1} (- 1)^{4} : 53

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (3)^{0} (- 1)^{5} : - 1

= 93 - 45 + 303 - 30 + 53 - 1

93 - 45 + 303 - 30 + 53 - 1 = 443 - 76

= 443 - 76

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Frequently Asked Questions (FAQ)

What is expand (sqrt(3)-1)^5 ?
The solution to expand (sqrt(3)-1)^5 is 44sqrt(3)-76