Question

Вариант 2 Представьте в виде многочлена выражение:
1) 2x(x4 – 5x3 + 3); 3) (7x – 3y)(2x + 5y);
2) (y + 2)(3y – 5); 4) (x – 1)(x2 – x – 2).
Разложите на множители:
1) 15xy – 25y2; 2) 12a5 – 4a4; 3) 6a – 6y + ab – by.
Решите уравнение 7x2 + 21x = 0.
Упростите выражение 3m(2m – 1) – (m + 3)(m – 2).
Решите уравнение: 1) (5x + 1)/6 – (x + 3)/4 = 3;
2) (4x – 1)(3x – 2) = (6x + 1)(2x + 3) – 4x.
Найдите значение выражения 18ab – 27a + 2b – 3, если a = –1 1/9, b = 1,2.
Докажите, что значение выражения 2165 – 367 кратно 5.
Разложите на множители трёхчлен x2 + 15x + 50.

Answer 1

1.

$2 x( {x}^{4} - 5 {x}^{3} + 3) = 2x \times {x}^{4} + 2x \times ( - 5 {x}^{3} ) \times 2x \times 3 = 2 {x}^{5} - 10 {x}^{4} + 6x$

$(y + 2)(3y - 5) = y \times 3y + y \times ( - 5) + 2 \times 3y + 2 \times ( - 5) = 3 {y}^{2} - 5y + 6y - 10 = 3 {y}^{2} + y - 10$

$(7x - 3y)(2x + 5y) = 7x \times 2x + 7x \times 5y - 3y \times 2x - 3y \times 5y = 14 {x}^{2} + 35xy - 6xy - 15 {y}^{2} = 14 {x}^{2} + 29xy - 15 {y}^{2}$

$(x - 1)( {x}^{2} - x - 2) = x \times {x}^{2} + x \times ( - x) + x \times ( - 2) - 1 \times {x}^{2} - 1 \times ( - x) - 1 \times ( - 2) = {x}^{3} - {x}^{2} - 2x - {x}^{2} + x + 2 = {x}^{3} - 2 {x}^{2} - x + 2$

2.

$15xy - 25 {y}^{2} = 5y(3x - 5y)$

$12 {a}^{5} - 4 {a}^{4} = 4{a}^{4} (3a - 1)$

$6a - 6y + ab - by = 6(a - y) + b(a - y) = (6 + b)(a - y)$

3.

$7 {x}^{2} + 21x = 0 \\ 7x(x + 3) = 0 \\ 1)7x = 0 \\ x = 0 \\ 2)x + 3 = 0 \\ x = - 3$

4.

$3m(2m - 1) - (m + 3)(m - 2) = 3m \times 2m + 3m \times ( - 1) - (m \times m + m \times ( -2) + 3 \times m + 3 \times ( - 2)) = 6 {m}^{2} - 3m - ( {m}^{2} - 2m + 3m - 6) = 6 {m}^{2} - 3m - {m}^{2} - m + 6 = 5 {m}^{2} - 4m + 6$

5.

$\frac{5x + 1}{6} - \frac{x + 3}{4} = 3 \\ \frac{(5x + 1) \times 2 - (x + 3) \times 3}{12} = \frac{3 \times 12}{12} \\ 10x + 2 - 3x - 9 = 36 \\ 7x - 7 = 36 \\ 7x = 36 + 7 \\ 7x = 43 \\ x = 43 \div 7 \\ x = 6 \frac{1}{7}$

$(4x - 1)(3x - 2) = (6x + 1)(2x + 3) - 4x \\ 12 {x}^{2} - 8x - 3x + 2 = 1 2{x}^{2} + 18x + 2x + 3 - 4x \\ 12 {x}^{2} - 11x + 2 - 12 {x}^{2} - 16x - 3 = 0 \\ - 27x - 1 = 0 \\ - 27x = 1 \\ x = - \frac{1}{27}$

6.

$18ab - 27a + 2b - 3 = 18 \times ( - 1 \frac{1}{9} ) \times 1.2 - 27 \times ( - 1 \frac{1}{9} ) + 2 \times 1.2 - 3 = 18 \times ( - \frac{10}{9}) \times 1.2 + 27 \times \frac{10}{9} + 2.4 - 3 = - 20 \times 1.2 + 30 - 0.6 = - 24 + 29.4 = 5.4$