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

The solution to expand (2x-y)^6 is 64x^6-192x^5y+240x^4y^2-160x^3y^3+60x^2y^4-12xy^5+y^6

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expand (2x-y)^6

expand

(2 x - y)^{6}

64 x^{6} - 192 x^{5} y + 240 x^{4} y^{2} - 160 x^{3} y^{3} + 60 x^{2} y^{4} - 12 x y^{5} + y^{6}

Solution steps

(2 x - y)^{6}

Apply binomial theorem:

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

a = 2 x, b = - y

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

Expand summation

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

Simplify

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

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} (2 x)^{5} (- y)^{1} : - 192 x^{5} y

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} (2 x)^{4} (- y)^{2} : 240 x^{4} y^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} (2 x)^{3} (- y)^{3} : - 160 x^{3} y^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} (2 x)^{2} (- y)^{4} : 60 x^{2} y^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} (2 x)^{1} (- y)^{5} : - 12 x y^{5}

Simplify

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

= 64 x^{6} - 192 x^{5} y + 240 x^{4} y^{2} - 160 x^{3} y^{3} + 60 x^{2} y^{4} - 12 x y^{5} + y^{6}

(3 a - 5)^{2}

lo g_{\frac{4}{5}} (\frac{125}{64})

32 m^{7} n^{11}

81 + - 32 + 49 - - 200

3267

What is expand (2x-y)^6 ?
The solution to expand (2x-y)^6 is 64x^6-192x^5y+240x^4y^2-160x^3y^3+60x^2y^4-12xy^5+y^6