What is expand (2sqrt(5)-2)^4 ?

The solution to expand (2sqrt(5)-2)^4 is 896-384sqrt(5)

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expand (2sqrt(5)-2)^4

expand

(25 - 2)^{4}

896 - 3845

Decimal Notation

37.34989 \dots

Solution steps

(25 - 2)^{4}

Apply binomial theorem:

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

a = 25, b = - 2

= i = 0 \sum 4 (i 4) (25)^{(4 - i)} (- 2)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (25)^{4} (- 2)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (25)^{3} (- 2)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (25)^{2} (- 2)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (25)^{1} (- 2)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (25)^{0} (- 2)^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (25)^{4} (- 2)^{0} : 400

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (25)^{3} (- 2)^{1} : - 3205

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (25)^{2} (- 2)^{2} : 480

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (25)^{1} (- 2)^{3} : - 645

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (25)^{0} (- 2)^{4} : 16

= 400 - 3205 + 480 - 645 + 16

400 - 3205 + 480 - 645 + 16 = 896 - 3845

= 896 - 3845

4 \cdot (x^{2} + 5)

\frac{x}{( x - 4 ) ( x - 5 )}

e^{t - 4} \cdot h (t - 4)

40 (y - \frac{5}{8} = \frac{3}{5} (x - \frac{1}{6}))

0.03 \cdot 3 (1. 2^{3})

What is expand (2sqrt(5)-2)^4 ?
The solution to expand (2sqrt(5)-2)^4 is 896-384sqrt(5)