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

The solution to expand (x^2-2y)^5 is x^{10}-10x^8y+40x^6y^2-80x^4y^3+80x^2y^4-32y^5

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expand (x^2-2y)^5

expand

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

x^{10} - 10 x^{8} y + 40 x^{6} y^{2} - 80 x^{4} y^{3} + 80 x^{2} y^{4} - 32 y^{5}

Solution steps

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

Apply binomial theorem:

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

a = x^{2}, b = - 2 y

= i = 0 \sum 5 (i 5) (x^{2})^{(5 - i)} (- 2 y)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (x^{2})^{5} (- 2 y)^{0} : x^{10}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (x^{2})^{4} (- 2 y)^{1} : - 10 x^{8} y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (x^{2})^{3} (- 2 y)^{2} : 40 x^{6} y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (x^{2})^{2} (- 2 y)^{3} : - 80 x^{4} y^{3}

Simplify

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

Simplify

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

= x^{10} - 10 x^{8} y + 40 x^{6} y^{2} - 80 x^{4} y^{3} + 80 x^{2} y^{4} - 32 y^{5}

4 a^{8} - 53 a^{4} b^{4} + 49 b^{8}

4 \frac{5}{2}

\frac{2}{2} \cdot 2

\frac{1}{y}

\frac{1}{u}

What is expand (x^2-2y)^5 ?
The solution to expand (x^2-2y)^5 is x^{10}-10x^8y+40x^6y^2-80x^4y^3+80x^2y^4-32y^5