What is expand (x-2y)^7 ?

The solution to expand (x-2y)^7 is x^7-14x^6y+84x^5y^2-280x^4y^3+560x^3y^4-672x^2y^5+448xy^6-128y^7

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expand (x-2y)^7

expand

(x - 2 y)^{7}

x^{7} - 14 x^{6} y + 84 x^{5} y^{2} - 280 x^{4} y^{3} + 560 x^{3} y^{4} - 672 x^{2} y^{5} + 448 x y^{6} - 128 y^{7}

Solution steps

(x - 2 y)^{7}

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 7 (i 7) x^{(7 - i)} (- 2 y)^{i}

Expand summation

= \frac{7 !}{0 ! ( 7 - 0 ) !} x^{7} (- 2 y)^{0} + \frac{7 !}{1 ! ( 7 - 1 ) !} x^{6} (- 2 y)^{1} + \frac{7 !}{2 ! ( 7 - 2 ) !} x^{5} (- 2 y)^{2} + \frac{7 !}{3 ! ( 7 - 3 ) !} x^{4} (- 2 y)^{3} + \frac{7 !}{4 ! ( 7 - 4 ) !} x^{3} (- 2 y)^{4} + \frac{7 !}{5 ! ( 7 - 5 ) !} x^{2} (- 2 y)^{5} + \frac{7 !}{6 ! ( 7 - 6 ) !} x^{1} (- 2 y)^{6} + \frac{7 !}{7 ! ( 7 - 7 ) !} x^{0} (- 2 y)^{7}

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} x^{7} (- 2 y)^{0} : x^{7}

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} x^{6} (- 2 y)^{1} : - 14 x^{6} y

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} x^{5} (- 2 y)^{2} : 84 x^{5} y^{2}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} x^{4} (- 2 y)^{3} : - 280 x^{4} y^{3}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} x^{3} (- 2 y)^{4} : 560 x^{3} y^{4}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} x^{2} (- 2 y)^{5} : - 672 x^{2} y^{5}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} x^{1} (- 2 y)^{6} : 448 x y^{6}

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} x^{0} (- 2 y)^{7} : - 128 y^{7}

= x^{7} - 14 x^{6} y + 84 x^{5} y^{2} - 280 x^{4} y^{3} + 560 x^{3} y^{4} - 672 x^{2} y^{5} + 448 x y^{6} - 128 y^{7}

m (m - 1) (m - 2) (m - 3)

5 \cdot 1 0^{7}

\frac{42}{9}

0. 3^{- 1}

\frac{37}{10}

What is expand (x-2y)^7 ?
The solution to expand (x-2y)^7 is x^7-14x^6y+84x^5y^2-280x^4y^3+560x^3y^4-672x^2y^5+448xy^6-128y^7