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Popular >

expand (3-sqrt(5))^5

Solution

expand

(3 - 5)^{5}

Solution

1968 - 8805

+1

Decimal Notation

0.26017 \dots

Solution steps

(3 - 5)^{5}

Apply binomial theorem:

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

a = 3, b = - 5

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

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 3^{5} (- 5)^{0} : 243

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 3^{4} (- 5)^{1} : - 4055

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 3^{3} (- 5)^{2} : 1350

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 3^{2} (- 5)^{3} : - 4505

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 3^{1} (- 5)^{4} : 375

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 3^{0} (- 5)^{5} : - 255

= 243 - 4055 + 1350 - 4505 + 375 - 255

243 - 4055 + 1350 - 4505 + 375 - 255 = 1968 - 8805

= 1968 - 8805

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Frequently Asked Questions (FAQ)

What is expand (3-sqrt(5))^5 ?
The solution to expand (3-sqrt(5))^5 is 1968-880sqrt(5)