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Popular >

expand (2-sqrt(3))^4

Solution

expand

(2 - 3)^{4}

Solution

97 - 563

+1

Decimal Notation

0.00515 \dots

Solution steps

(2 - 3)^{4}

Apply binomial theorem:

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

a = 2, b = - 3

= i = 0 \sum 4 (i 4) \cdot 2^{(4 - i)} (- 3)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 2^{4} (- 3)^{0} : 16

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 2^{3} (- 3)^{1} : - 323

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 2^{2} (- 3)^{2} : 72

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 2^{1} (- 3)^{3} : - 243

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 2^{0} (- 3)^{4} : 9

= 16 - 323 + 72 - 243 + 9

16 - 323 + 72 - 243 + 9 = 97 - 563

= 97 - 563

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Frequently Asked Questions (FAQ)

What is expand (2-sqrt(3))^4 ?
The solution to expand (2-sqrt(3))^4 is 97-56sqrt(3)