What is expand (-3+sqrt(5))^8 ?

The solution to expand (-3+sqrt(5))^8 is 282496-126336sqrt(5)

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expand (-3+sqrt(5))^8

expand

(- 3 + 5)^{8}

282496 - 1263365

Decimal Notation

0.11599 \dots

Solution steps

(- 3 + 5)^{8}

Apply binomial theorem:

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

a = - 3, b = 5

= i = 0 \sum 8 (i 8) (- 3)^{(8 - i)} (5)^{i}

Expand summation

= \frac{8 !}{0 ! ( 8 - 0 ) !} (- 3)^{8} (5)^{0} + \frac{8 !}{1 ! ( 8 - 1 ) !} (- 3)^{7} (5)^{1} + \frac{8 !}{2 ! ( 8 - 2 ) !} (- 3)^{6} (5)^{2} + \frac{8 !}{3 ! ( 8 - 3 ) !} (- 3)^{5} (5)^{3} + \frac{8 !}{4 ! ( 8 - 4 ) !} (- 3)^{4} (5)^{4} + \frac{8 !}{5 ! ( 8 - 5 ) !} (- 3)^{3} (5)^{5} + \frac{8 !}{6 ! ( 8 - 6 ) !} (- 3)^{2} (5)^{6} + \frac{8 !}{7 ! ( 8 - 7 ) !} (- 3)^{1} (5)^{7} + \frac{8 !}{8 ! ( 8 - 8 ) !} (- 3)^{0} (5)^{8}

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} (- 3)^{8} (5)^{0} : 6561

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} (- 3)^{7} (5)^{1} : - 174965

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} (- 3)^{6} (5)^{2} : 102060

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} (- 3)^{5} (5)^{3} : - 680405

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} (- 3)^{4} (5)^{4} : 141750

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} (- 3)^{3} (5)^{5} : - 378005

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} (- 3)^{2} (5)^{6} : 31500

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} (- 3)^{1} (5)^{7} : - 30005

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} (- 3)^{0} (5)^{8} : 625

= 6561 - 174965 + 102060 - 680405 + 141750 - 378005 + 31500 - 30005 + 625

6561 - 174965 + 102060 - 680405 + 141750 - 378005 + 31500 - 30005 + 625 = 282496 - 1263365

= 282496 - 1263365

(5 + 7) (7 + 5 - 2)

(a + 2) (5 a + b)

(x - 4) (9 - x^{2})

\frac{e ^{- 3 π s}}{s ( s ^{2} + 1 )}

\frac{0.06325}{j ( 6.4821 j + 0.004 j ^{31.62} + 1 )}

What is expand (-3+sqrt(5))^8 ?
The solution to expand (-3+sqrt(5))^8 is 282496-126336sqrt(5)