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Popular >

expand (2-sqrt(2))^5

Solution

expand

(2 - 2)^{5}

Solution

232 - 1642

+1

Decimal Notation

0.06897 \dots

Solution steps

(2 - 2)^{5}

Apply binomial theorem:

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

a = 2, b = - 2

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

Expand summation

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

Simplify

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

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 2^{4} (- 2)^{1} : - 802

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 2^{3} (- 2)^{2} : 160

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 2^{2} (- 2)^{3} : - 802

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 2^{1} (- 2)^{4} : 40

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 2^{0} (- 2)^{5} : - 42

= 32 - 802 + 160 - 802 + 40 - 42

32 - 802 + 160 - 802 + 40 - 42 = 232 - 1642

= 232 - 1642

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Frequently Asked Questions (FAQ)

What is expand (2-sqrt(2))^5 ?
The solution to expand (2-sqrt(2))^5 is 232-164sqrt(2)