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Popular >

expand (sqrt(2)+y)^{12}

Solution

expand

(2 + y)^{12}

Solution

64 + 3842 y + 2112 y^{2} + 35202 y^{3} + 7920 y^{4} + 63362 y^{5} + 7392 y^{6} + 31682 y^{7} + 1980 y^{8} + 4402 y^{9} + 132 y^{10} + 122 y^{11} + y^{12}

Solution steps

(2 + y)^{12}

Apply binomial theorem:

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

a = 2, b = y

= i = 0 \sum 12 (i 12) (2)^{(12 - i)} y^{i}

Expand summation

= \frac{12 !}{0 ! ( 12 - 0 ) !} (2)^{12} y^{0} + \frac{12 !}{1 ! ( 12 - 1 ) !} (2)^{11} y^{1} + \frac{12 !}{2 ! ( 12 - 2 ) !} (2)^{10} y^{2} + \frac{12 !}{3 ! ( 12 - 3 ) !} (2)^{9} y^{3} + \frac{12 !}{4 ! ( 12 - 4 ) !} (2)^{8} y^{4} + \frac{12 !}{5 ! ( 12 - 5 ) !} (2)^{7} y^{5} + \frac{12 !}{6 ! ( 12 - 6 ) !} (2)^{6} y^{6} + \frac{12 !}{7 ! ( 12 - 7 ) !} (2)^{5} y^{7} + \frac{12 !}{8 ! ( 12 - 8 ) !} (2)^{4} y^{8} + \frac{12 !}{9 ! ( 12 - 9 ) !} (2)^{3} y^{9} + \frac{12 !}{10 ! ( 12 - 10 ) !} (2)^{2} y^{10} + \frac{12 !}{11 ! ( 12 - 11 ) !} (2)^{1} y^{11} + \frac{12 !}{12 ! ( 12 - 12 ) !} (2)^{0} y^{12}

Simplify

\frac{12 !}{0 ! ( 12 - 0 ) !} (2)^{12} y^{0} : 64

Simplify

\frac{12 !}{1 ! ( 12 - 1 ) !} (2)^{11} y^{1} : 3842 y

Simplify

\frac{12 !}{2 ! ( 12 - 2 ) !} (2)^{10} y^{2} : 2112 y^{2}

Simplify

\frac{12 !}{3 ! ( 12 - 3 ) !} (2)^{9} y^{3} : 35202 y^{3}

Simplify

\frac{12 !}{4 ! ( 12 - 4 ) !} (2)^{8} y^{4} : 7920 y^{4}

Simplify

\frac{12 !}{5 ! ( 12 - 5 ) !} (2)^{7} y^{5} : 63362 y^{5}

Simplify

\frac{12 !}{6 ! ( 12 - 6 ) !} (2)^{6} y^{6} : 7392 y^{6}

Simplify

\frac{12 !}{7 ! ( 12 - 7 ) !} (2)^{5} y^{7} : 31682 y^{7}

Simplify

\frac{12 !}{8 ! ( 12 - 8 ) !} (2)^{4} y^{8} : 1980 y^{8}

Simplify

\frac{12 !}{9 ! ( 12 - 9 ) !} (2)^{3} y^{9} : 4402 y^{9}

Simplify

\frac{12 !}{10 ! ( 12 - 10 ) !} (2)^{2} y^{10} : 132 y^{10}

Simplify

\frac{12 !}{11 ! ( 12 - 11 ) !} (2)^{1} y^{11} : 122 y^{11}

Simplify

\frac{12 !}{12 ! ( 12 - 12 ) !} (2)^{0} y^{12} : y^{12}

= 64 + 3842 y + 2112 y^{2} + 35202 y^{3} + 7920 y^{4} + 63362 y^{5} + 7392 y^{6} + 31682 y^{7} + 1980 y^{8} + 4402 y^{9} + 132 y^{10} + 122 y^{11} + y^{12}

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Frequently Asked Questions (FAQ)

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