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

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

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expand (2x-3y)^6

expand

(2 x - 3 y)^{6}

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

Solution steps

(2 x - 3 y)^{6}

Apply binomial theorem:

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

a = 2 x, b = - 3 y

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

121 - 49 x^{6} y^{2}

16 \times 4

- 327 + 212

\frac{x ^{2} - 2 x - 15}{5 - x}

(3 x^{\frac{1}{2}} y^{2})^{4}

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