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Popular >

expand (3x+y)^{11}

Solution

expand

(3 x + y)^{11}

Solution

177147 x^{11} + 649539 x^{10} y + 1082565 x^{9} y^{2} + 1082565 x^{8} y^{3} + 721710 x^{7} y^{4} + 336798 x^{6} y^{5} + 112266 x^{5} y^{6} + 26730 x^{4} y^{7} + 4455 x^{3} y^{8} + 495 x^{2} y^{9} + 33 x y^{10} + y^{11}

Solution steps

(3 x + y)^{11}

Apply binomial theorem:

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

a = 3 x, b = y

= i = 0 \sum 11 (i 11) (3 x)^{(11 - i)} y^{i}

Expand summation

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

Simplify

\frac{11 !}{0 ! ( 11 - 0 ) !} (3 x)^{11} y^{0} : 177147 x^{11}

Simplify

\frac{11 !}{1 ! ( 11 - 1 ) !} (3 x)^{10} y^{1} : 649539 x^{10} y

Simplify

\frac{11 !}{2 ! ( 11 - 2 ) !} (3 x)^{9} y^{2} : 1082565 x^{9} y^{2}

Simplify

\frac{11 !}{3 ! ( 11 - 3 ) !} (3 x)^{8} y^{3} : 1082565 x^{8} y^{3}

Simplify

\frac{11 !}{4 ! ( 11 - 4 ) !} (3 x)^{7} y^{4} : 721710 x^{7} y^{4}

Simplify

\frac{11 !}{5 ! ( 11 - 5 ) !} (3 x)^{6} y^{5} : 336798 x^{6} y^{5}

Simplify

\frac{11 !}{6 ! ( 11 - 6 ) !} (3 x)^{5} y^{6} : 112266 x^{5} y^{6}

Simplify

\frac{11 !}{7 ! ( 11 - 7 ) !} (3 x)^{4} y^{7} : 26730 x^{4} y^{7}

Simplify

\frac{11 !}{8 ! ( 11 - 8 ) !} (3 x)^{3} y^{8} : 4455 x^{3} y^{8}

Simplify

\frac{11 !}{9 ! ( 11 - 9 ) !} (3 x)^{2} y^{9} : 495 x^{2} y^{9}

Simplify

\frac{11 !}{10 ! ( 11 - 10 ) !} (3 x)^{1} y^{10} : 33 x y^{10}

Simplify

\frac{11 !}{11 ! ( 11 - 11 ) !} (3 x)^{0} y^{11} : y^{11}

= 177147 x^{11} + 649539 x^{10} y + 1082565 x^{9} y^{2} + 1082565 x^{8} y^{3} + 721710 x^{7} y^{4} + 336798 x^{6} y^{5} + 112266 x^{5} y^{6} + 26730 x^{4} y^{7} + 4455 x^{3} y^{8} + 495 x^{2} y^{9} + 33 x y^{10} + y^{11}

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Frequently Asked Questions (FAQ)

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