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}

15 \frac{3}{10} - \frac{2}{5}

\frac{- 7}{- 3 - 11}

7 x^{2} + 21 x - 28

lo g_{10} (\frac{1}{6})

\frac{x ^{2} + 11 x + 28}{x ^{2} + x - 12}

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