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Popular >

expand (1+sqrt(5))^4

Solution

expand

(1 + 5)^{4}

Solution

56 + 245

+1

Decimal Notation

109.66563 \dots

Solution steps

(1 + 5)^{4}

Apply binomial theorem:

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

a = 1, b = 5

= i = 0 \sum 4 (i 4) \cdot 1^{(4 - i)} (5)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} (5)^{0} : 1

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 1^{3} (5)^{1} : 45

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 1^{2} (5)^{2} : 30

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 1^{1} (5)^{3} : 205

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (5)^{4} : 25

= 1 + 45 + 30 + 205 + 25

1 + 45 + 30 + 205 + 25 = 56 + 245

= 56 + 245

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Frequently Asked Questions (FAQ)

What is expand (1+sqrt(5))^4 ?
The solution to expand (1+sqrt(5))^4 is 56+24sqrt(5)