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Popular >

expand (1-sqrt(3))^4

Solution

expand

(1 - 3)^{4}

Solution

28 - 163

+1

Decimal Notation

0.28718 \dots

Solution steps

(1 - 3)^{4}

Apply binomial theorem:

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

a = 1, b = - 3

= i = 0 \sum 4 (i 4) \cdot 1^{(4 - i)} (- 3)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} (- 3)^{0} : 1

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 1^{3} (- 3)^{1} : - 43

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 1^{2} (- 3)^{2} : 18

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 1^{1} (- 3)^{3} : - 123

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (- 3)^{4} : 9

= 1 - 43 + 18 - 123 + 9

1 - 43 + 18 - 123 + 9 = 28 - 163

= 28 - 163

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Frequently Asked Questions (FAQ)

What is expand (1-sqrt(3))^4 ?
The solution to expand (1-sqrt(3))^4 is 28-16sqrt(3)