What is expand (3x+2y)^6 ?

The solution to expand (3x+2y)^6 is 729x^6+2916x^5y+4860x^4y^2+4320x^3y^3+2160x^2y^4+576xy^5+64y^6

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expand (3x+2y)^6

expand

(3 x + 2 y)^{6}

729 x^{6} + 2916 x^{5} y + 4860 x^{4} y^{2} + 4320 x^{3} y^{3} + 2160 x^{2} y^{4} + 576 x y^{5} + 64 y^{6}

Solution steps

(3 x + 2 y)^{6}

Apply binomial theorem:

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

a = 3 x, b = 2 y

= i = 0 \sum 6 (i 6) (3 x)^{(6 - i)} (2 y)^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} (3 x)^{6} (2 y)^{0} : 729 x^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} (3 x)^{5} (2 y)^{1} : 2916 x^{5} y

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} (3 x)^{4} (2 y)^{2} : 4860 x^{4} y^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} (3 x)^{3} (2 y)^{3} : 4320 x^{3} y^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} (3 x)^{2} (2 y)^{4} : 2160 x^{2} y^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} (3 x)^{1} (2 y)^{5} : 576 x y^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} (3 x)^{0} (2 y)^{6} : 64 y^{6}

= 729 x^{6} + 2916 x^{5} y + 4860 x^{4} y^{2} + 4320 x^{3} y^{3} + 2160 x^{2} y^{4} + 576 x y^{5} + 64 y^{6}

4 x^{4} + 9 x^{3} - 5 x^{2} + 9 x - 9

\frac{2}{9} - \frac{1}{9}

\frac{10}{5} + \frac{9}{10}

f (x) = \frac{4 x ^{3} + 16 x ^{2} - 29 x + 10}{2 x - 1}

+ 4 c^{2} - 1

What is expand (3x+2y)^6 ?
The solution to expand (3x+2y)^6 is 729x^6+2916x^5y+4860x^4y^2+4320x^3y^3+2160x^2y^4+576xy^5+64y^6