What is expand (5+2sqrt(7))^4 ?

The solution to expand (5+2sqrt(7))^4 is 5609+2120sqrt(7)

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expand (5+2sqrt(7))^4

expand

(5 + 27)^{4}

5609 + 21207

Decimal Notation

11217.99277 \dots

Solution steps

(5 + 27)^{4}

Apply binomial theorem:

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

a = 5, b = 27

= i = 0 \sum 4 (i 4) \cdot 5^{(4 - i)} (27)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 5^{4} (27)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 5^{3} (27)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 5^{2} (27)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 5^{1} (27)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 5^{0} (27)^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 5^{4} (27)^{0} : 625

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 5^{3} (27)^{1} : 10007

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 5^{2} (27)^{2} : 4200

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 5^{1} (27)^{3} : 11207

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 5^{0} (27)^{4} : 784

= 625 + 10007 + 4200 + 11207 + 784

625 + 10007 + 4200 + 11207 + 784 = 5609 + 21207

= 5609 + 21207

P (- 7, 3) Q (4, - 8)

(x^{2} - 1) y^{''} (x) + x y^{'} (x) - y

5 (1 + Δ t)^{2}

(c - 1) (c + 2) (c + 6) (c - 6)

\frac{7 ( 12 e + 19 e ^{\frac{19}{12}} )}{288}

What is expand (5+2sqrt(7))^4 ?
The solution to expand (5+2sqrt(7))^4 is 5609+2120sqrt(7)