What is expand (3x-x^2)^5 ?

The solution to expand (3x-x^2)^5 is 243x^5-405x^6+270x^7-90x^8+15x^9-x^{10}

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expand (3x-x^2)^5

expand

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

243 x^{5} - 405 x^{6} + 270 x^{7} - 90 x^{8} + 15 x^{9} - x^{10}

Solution steps

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

Apply binomial theorem:

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

a = 3 x, b = - x^{2}

= i = 0 \sum 5 (i 5) (3 x)^{(5 - i)} (- x^{2})^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (3 x)^{5} (- x^{2})^{0} : 243 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (3 x)^{4} (- x^{2})^{1} : - 405 x^{6}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (3 x)^{3} (- x^{2})^{2} : 270 x^{7}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (3 x)^{2} (- x^{2})^{3} : - 90 x^{8}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (3 x)^{1} (- x^{2})^{4} : 15 x^{9}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (3 x)^{0} (- x^{2})^{5} : - x^{10}

= 243 x^{5} - 405 x^{6} + 270 x^{7} - 90 x^{8} + 15 x^{9} - x^{10}

x^{4} + 11 x^{2} + 36

m + 0.5 + m + 0.5 + 2 m + 2 m + 8

x^{2} (y^{2} - x y^{2} + 1) - (x^{3} + x^{2} + 1) \cdot y^{2}

(- 2 x^{4})^{2}

- x - 10

What is expand (3x-x^2)^5 ?
The solution to expand (3x-x^2)^5 is 243x^5-405x^6+270x^7-90x^8+15x^9-x^{10}