What is expand (3sqrt(2)-sqrt(3))^5 ?

The solution to expand (3sqrt(2)-sqrt(3))^5 is 2727sqrt(2)-2169sqrt(3)

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expand (3sqrt(2)-sqrt(3))^5

expand

(32 - 3)^{5}

27272 - 21693

Decimal Notation

99.74218 \dots

Solution steps

(32 - 3)^{5}

Apply binomial theorem:

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

a = 32, b = - 3

= i = 0 \sum 5 (i 5) (32)^{(5 - i)} (- 3)^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} (32)^{5} (- 3)^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (32)^{4} (- 3)^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (32)^{3} (- 3)^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (32)^{2} (- 3)^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (32)^{1} (- 3)^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (32)^{0} (- 3)^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (32)^{5} (- 3)^{0} : 9722

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (32)^{4} (- 3)^{1} : - 16203

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (32)^{3} (- 3)^{2} : 16202

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (32)^{2} (- 3)^{3} : - 5403

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (32)^{1} (- 3)^{4} : 1352

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (32)^{0} (- 3)^{5} : - 93

= 9722 - 16203 + 16202 - 5403 + 1352 - 93

9722 - 16203 + 16202 - 5403 + 1352 - 93 = 27272 - 21693

= 27272 - 21693

e^{(1 + i) t}

2 x (x - 2)

(a + h + a + h)^{2}

\frac{x ^{2} - 11 x + 6}{( x + 2 ) ( x ^{2} - 4 x + 4 )}

A (- 2, - 3) B (- 2, 3)

What is expand (3sqrt(2)-sqrt(3))^5 ?
The solution to expand (3sqrt(2)-sqrt(3))^5 is 2727sqrt(2)-2169sqrt(3)