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Popular >

expand (3+sqrt(7))^4

Solution

expand

(3 + 7)^{4}

Solution

508 + 1927

+1

Decimal Notation

1015.98425 \dots

Solution steps

(3 + 7)^{4}

Apply binomial theorem:

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

a = 3, b = 7

= i = 0 \sum 4 (i 4) \cdot 3^{(4 - i)} (7)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 3^{4} (7)^{0} : 81

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 3^{3} (7)^{1} : 1087

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 3^{2} (7)^{2} : 378

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 3^{1} (7)^{3} : 847

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 3^{0} (7)^{4} : 49

= 81 + 1087 + 378 + 847 + 49

81 + 1087 + 378 + 847 + 49 = 508 + 1927

= 508 + 1927

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Frequently Asked Questions (FAQ)

What is expand (3+sqrt(7))^4 ?
The solution to expand (3+sqrt(7))^4 is 508+192sqrt(7)