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Popular >

expand (3y+2x)^{10}

Solution

expand

(3 y + 2 x)^{10}

Solution

59049 y^{10} + 393660 y^{9} x + 1180980 y^{8} x^{2} + 2099520 y^{7} x^{3} + 2449440 y^{6} x^{4} + 1959552 y^{5} x^{5} + 1088640 y^{4} x^{6} + 414720 y^{3} x^{7} + 103680 y^{2} x^{8} + 15360 y x^{9} + 1024 x^{10}

Solution steps

(3 y + 2 x)^{10}

Apply binomial theorem:

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

a = 3 y, b = 2 x

= i = 0 \sum 10 (i 10) (3 y)^{(10 - i)} (2 x)^{i}

Expand summation

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

Simplify

\frac{10 !}{0 ! ( 10 - 0 ) !} (3 y)^{10} (2 x)^{0} : 59049 y^{10}

Simplify

\frac{10 !}{1 ! ( 10 - 1 ) !} (3 y)^{9} (2 x)^{1} : 393660 y^{9} x

Simplify

\frac{10 !}{2 ! ( 10 - 2 ) !} (3 y)^{8} (2 x)^{2} : 1180980 y^{8} x^{2}

Simplify

\frac{10 !}{3 ! ( 10 - 3 ) !} (3 y)^{7} (2 x)^{3} : 2099520 y^{7} x^{3}

Simplify

\frac{10 !}{4 ! ( 10 - 4 ) !} (3 y)^{6} (2 x)^{4} : 2449440 y^{6} x^{4}

Simplify

\frac{10 !}{5 ! ( 10 - 5 ) !} (3 y)^{5} (2 x)^{5} : 1959552 y^{5} x^{5}

Simplify

\frac{10 !}{6 ! ( 10 - 6 ) !} (3 y)^{4} (2 x)^{6} : 1088640 y^{4} x^{6}

Simplify

\frac{10 !}{7 ! ( 10 - 7 ) !} (3 y)^{3} (2 x)^{7} : 414720 y^{3} x^{7}

Simplify

\frac{10 !}{8 ! ( 10 - 8 ) !} (3 y)^{2} (2 x)^{8} : 103680 y^{2} x^{8}

Simplify

\frac{10 !}{9 ! ( 10 - 9 ) !} (3 y)^{1} (2 x)^{9} : 15360 y x^{9}

Simplify

\frac{10 !}{10 ! ( 10 - 10 ) !} (3 y)^{0} (2 x)^{10} : 1024 x^{10}

= 59049 y^{10} + 393660 y^{9} x + 1180980 y^{8} x^{2} + 2099520 y^{7} x^{3} + 2449440 y^{6} x^{4} + 1959552 y^{5} x^{5} + 1088640 y^{4} x^{6} + 414720 y^{3} x^{7} + 103680 y^{2} x^{8} + 15360 y x^{9} + 1024 x^{10}

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