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Popular >

expand (sqrt(2)-1)^4

Solution

expand

(2 - 1)^{4}

Solution

17 - 122

+1

Decimal Notation

0.02943 \dots

Solution steps

(2 - 1)^{4}

Apply binomial theorem:

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

a = 2, b = - 1

= i = 0 \sum 4 (i 4) (2)^{(4 - i)} (- 1)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (2)^{4} (- 1)^{0} : 4

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (2)^{3} (- 1)^{1} : - 82

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (2)^{2} (- 1)^{2} : 12

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (2)^{1} (- 1)^{3} : - 42

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (2)^{0} (- 1)^{4} : 1

= 4 - 82 + 12 - 42 + 1

4 - 82 + 12 - 42 + 1 = 17 - 122

= 17 - 122

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Frequently Asked Questions (FAQ)

What is expand (sqrt(2)-1)^4 ?
The solution to expand (sqrt(2)-1)^4 is 17-12sqrt(2)