Question

Помогите пожалуйста с алгеброй.Комбинаторика​

Answer 1

Ответ:

Бином Ньютона:

${(a + b)}^{n} = C_{n}^{0} \times {a}^{n} + C_{n}^{1} \times {a}^{n - 1} \times b + C_{n}^{2} \times {a}^{n - 2} \times {b}^{2} + \dots + C_{n}^{n} \times {b}^{n}$

$C_{n}^{m} = \frac{n!}{m!(n - m)!}$

$n! = 1 \times 2 \times 3 \times 4 \times \dots \times n$

${(3a - 5x)}^{5} = C_{5}^{0} \times {(3a)}^{5} - C_{5}^{1} \times {(3a)}^{4} \times 5x + C_{5}^{2} \times {(3a)}^{3} \times {(5x)}^{2} - C_{5}^{3} \times {(3a)}^{2} \times {(5x)}^{3} + C_{5}^{4} \times 3a \times {(5x)}^{4} - C_{5}^{5} \times {(5x)}^{5}$

Третий член:

$C_{5}^{2} \times 27 {a}^{3} \times 25 {x}^{2} = \frac{5!}{2!(5 - 2)!} \times 27 {a}^{3} \times 25 {x}^{2} = \\ \frac{3! \times 4 \times 5}{1 \times 2 \times 3!} \times 27 {a}^{3} \times 25 {x}^{2} = 10 \times 675 {a}^{3} {x}^{2} = 6750 {a}^{3} {x}^{2}$

Ответ: 6750a³x²