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Popular >

expand (sqrt(2)-1)^5

Solution

expand

(2 - 1)^{5}

Solution

292 - 41

+1

Solution steps

(2 - 1)^{5}

Apply binomial theorem:

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

a = 2, b = - 1

= i = 0 \sum 5 (i 5) (2)^{(5 - i)} (- 1)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (2)^{5} (- 1)^{0} : 42

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (2)^{4} (- 1)^{1} : - 20

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (2)^{3} (- 1)^{2} : 202

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (2)^{2} (- 1)^{3} : - 20

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (2)^{1} (- 1)^{4} : 52

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (2)^{0} (- 1)^{5} : - 1

= 42 - 20 + 202 - 20 + 52 - 1

42 - 20 + 202 - 20 + 52 - 1 = 292 - 41

= 292 - 41

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Frequently Asked Questions (FAQ)

What is expand (sqrt(2)-1)^5 ?
The solution to expand (sqrt(2)-1)^5 is 29sqrt(2)-41