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Popular >

expand (2-sqrt(3))^5

Solution

expand

(2 - 3)^{5}

Solution

362 - 2093

+1

Decimal Notation

0.00138 \dots

Solution steps

(2 - 3)^{5}

Apply binomial theorem:

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

a = 2, b = - 3

= i = 0 \sum 5 (i 5) \cdot 2^{(5 - i)} (- 3)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 2^{5} (- 3)^{0} : 32

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 2^{4} (- 3)^{1} : - 803

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 2^{3} (- 3)^{2} : 240

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 2^{2} (- 3)^{3} : - 1203

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 2^{1} (- 3)^{4} : 90

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 2^{0} (- 3)^{5} : - 93

= 32 - 803 + 240 - 1203 + 90 - 93

32 - 803 + 240 - 1203 + 90 - 93 = 362 - 2093

= 362 - 2093

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expand ((((2y+3)/5))/(2))^2 expand

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Frequently Asked Questions (FAQ)

What is expand (2-sqrt(3))^5 ?
The solution to expand (2-sqrt(3))^5 is 362-209sqrt(3)