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Popular >

expand (1+sqrt(3))^8

Solution

expand

(1 + 3)^{8}

Solution

1552 + 8963

+1

Decimal Notation

3103.91752 \dots

Solution steps

(1 + 3)^{8}

Apply binomial theorem:

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

a = 1, b = 3

= i = 0 \sum 8 (i 8) \cdot 1^{(8 - i)} (3)^{i}

Expand summation

= \frac{8 !}{0 ! ( 8 - 0 ) !} \cdot 1^{8} (3)^{0} + \frac{8 !}{1 ! ( 8 - 1 ) !} \cdot 1^{7} (3)^{1} + \frac{8 !}{2 ! ( 8 - 2 ) !} \cdot 1^{6} (3)^{2} + \frac{8 !}{3 ! ( 8 - 3 ) !} \cdot 1^{5} (3)^{3} + \frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 1^{4} (3)^{4} + \frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 1^{3} (3)^{5} + \frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 1^{2} (3)^{6} + \frac{8 !}{7 ! ( 8 - 7 ) !} \cdot 1^{1} (3)^{7} + \frac{8 !}{8 ! ( 8 - 8 ) !} \cdot 1^{0} (3)^{8}

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} \cdot 1^{8} (3)^{0} : 1

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} \cdot 1^{7} (3)^{1} : 83

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} \cdot 1^{6} (3)^{2} : 84

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} \cdot 1^{5} (3)^{3} : 1683

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 1^{4} (3)^{4} : 630

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 1^{3} (3)^{5} : 5043

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 1^{2} (3)^{6} : 756

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} \cdot 1^{1} (3)^{7} : 2163

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} \cdot 1^{0} (3)^{8} : 81

= 1 + 83 + 84 + 1683 + 630 + 5043 + 756 + 2163 + 81

1 + 83 + 84 + 1683 + 630 + 5043 + 756 + 2163 + 81 = 1552 + 8963

= 1552 + 8963

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Frequently Asked Questions (FAQ)

What is expand (1+sqrt(3))^8 ?
The solution to expand (1+sqrt(3))^8 is 1552+896sqrt(3)