What is expand (a-3)^5 ?

The solution to expand (a-3)^5 is a^5-15a^4+90a^3-270a^2+405a-243

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expand (a-3)^5

expand

(a - 3)^{5}

a^{5} - 15 a^{4} + 90 a^{3} - 270 a^{2} + 405 a - 243

Solution steps

(a - 3)^{5}

Apply binomial theorem:

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

a = a, b = - 3

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

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} a^{5} (- 3)^{0} : a^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} a^{4} (- 3)^{1} : - 15 a^{4}

Simplify

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

Simplify

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

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} a^{1} (- 3)^{4} : 405 a

Simplify

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

= a^{5} - 15 a^{4} + 90 a^{3} - 270 a^{2} + 405 a - 243

(- 1 - i)^{16}

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

14 + 83

\frac{7 - 3 i}{i}

(312)^{2}

What is expand (a-3)^5 ?
The solution to expand (a-3)^5 is a^5-15a^4+90a^3-270a^2+405a-243