What is expand (x-2y)^5 ?

The solution to expand (x-2y)^5 is x^5-10x^4y+40x^3y^2-80x^2y^3+80xy^4-32y^5

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expand (x-2y)^5

expand

(x - 2 y)^{5}

x^{5} - 10 x^{4} y + 40 x^{3} y^{2} - 80 x^{2} y^{3} + 80 x y^{4} - 32 y^{5}

Solution steps

(x - 2 y)^{5}

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 5 (i 5) x^{(5 - i)} (- 2 y)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} x^{5} (- 2 y)^{0} : x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} (- 2 y)^{1} : - 10 x^{4} y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} (- 2 y)^{2} : 40 x^{3} y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} (- 2 y)^{3} : - 80 x^{2} y^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} (- 2 y)^{4} : 80 x y^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} (- 2 y)^{5} : - 32 y^{5}

= x^{5} - 10 x^{4} y + 40 x^{3} y^{2} - 80 x^{2} y^{3} + 80 x y^{4} - 32 y^{5}

(x^{2} + 2 x - 5) - (3 x^{2} - 4 x + 7)

\frac{cos ( θ )}{sin ( θ )} + \frac{sin ( θ )}{cos ( θ )}

9. 8^{2}

\frac{10}{1 + 2 i}

3 x^{3} - x^{2} \times (- 2) x

What is expand (x-2y)^5 ?
The solution to expand (x-2y)^5 is x^5-10x^4y+40x^3y^2-80x^2y^3+80xy^4-32y^5