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Popular >

expand (sqrt(5)+2)^4

Solution

expand

(5 + 2)^{4}

Solution

161 + 725

+1

Decimal Notation

321.99689 \dots

Solution steps

(5 + 2)^{4}

Apply binomial theorem:

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

a = 5, b = 2

= i = 0 \sum 4 (i 4) (5)^{(4 - i)} \cdot 2^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (5)^{4} \cdot 2^{0} : 25

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (5)^{3} \cdot 2^{1} : 405

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (5)^{2} \cdot 2^{2} : 120

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (5)^{1} \cdot 2^{3} : 325

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (5)^{0} \cdot 2^{4} : 16

= 25 + 405 + 120 + 325 + 16

25 + 405 + 120 + 325 + 16 = 161 + 725

= 161 + 725

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Frequently Asked Questions (FAQ)

What is expand (sqrt(5)+2)^4 ?
The solution to expand (sqrt(5)+2)^4 is 161+72sqrt(5)