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Popular >

expand (1-sqrt(2))^4

Solution

expand

(1 - 2)^{4}

Solution

17 - 122

+1

Decimal Notation

0.02943 \dots

Solution steps

(1 - 2)^{4}

Apply binomial theorem:

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

a = 1, b = - 2

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

= 1 - 42 + 12 - 82 + 4

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

= 17 - 122

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Frequently Asked Questions (FAQ)

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