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Popular >

expand (1+sqrt(3))^6

Solution

expand

(1 + 3)^{6}

Solution

208 + 1203

+1

Decimal Notation

415.84609 \dots

Solution steps

(1 + 3)^{6}

Apply binomial theorem:

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

a = 1, b = 3

= i = 0 \sum 6 (i 6) \cdot 1^{(6 - i)} (3)^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 1^{6} (3)^{0} : 1

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 1^{5} (3)^{1} : 63

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 1^{4} (3)^{2} : 45

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 1^{3} (3)^{3} : 603

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 1^{2} (3)^{4} : 135

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 1^{1} (3)^{5} : 543

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 1^{0} (3)^{6} : 27

= 1 + 63 + 45 + 603 + 135 + 543 + 27

1 + 63 + 45 + 603 + 135 + 543 + 27 = 208 + 1203

= 208 + 1203

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Frequently Asked Questions (FAQ)

What is expand (1+sqrt(3))^6 ?
The solution to expand (1+sqrt(3))^6 is 208+120sqrt(3)