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

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

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expand (x-2y)^6

expand

(x - 2 y)^{6}

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

Solution steps

(x - 2 y)^{6}

Apply binomial theorem:

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

a = x, b = - 2 y

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{5}{15 b - b}

5 x y (x + 1) + 10 x (x + 1)

24 x^{2} \cdot y + 36 x^{3} \cdot y^{2} - 12 x^{4} \cdot y^{3}

((15 0^{y})^{2})^{3}

m^{5} \cdot m^{3} \cdot m^{- 4}

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