Question

Вынесение общего множителя за скобки

Вариант 3
1. 15х + 18y
2. 3хy – 5y
3. a4 + a3
4. 2y5 – 4y3
5. 5ab + 10a2
6. ax2 + 3ax
7. xy3 + 5x2y2 – 3x2y
8. 5(2 - a) + 3a(2 - a)
9. x(x – y) – 3(y – x)

10. 10m5n2 + 15nm7
11. 8x6y2 + 24y2x3 – 16x5y5
12. (x – 3)(3x + 1) + (3 – x)(3 + x)
13. a3(a + 6)2 – 3a4(6 + a)

Answer 1

1. 15х + 18y = 3(5x + 6y).

2. 3хy – 5y = y(3x – 5).

3. a⁴ + a³ = a³(a + 1).

4. 2y⁵ – 4y³ = 2y³(y² – 2).

5. 5ab + 10a² = 5a(b + 2a).

6. ax² + 3ax = ax(x + 3).

7. xy³ + 5x²y² – 3x²y = xy(y² + 5xy – 3x).

8. 5(2 – a) + 3a(2 – a) = (2 – a)(5 + 3a).

9. x(x – y) – 3(y – x) = x(x – y) + 3(x – y) = (x – y)(x + 3).

10. 10m⁵n² + 15nm⁷ = 5m⁵n(2n + 3m²).

11. 8x⁶y² + 24y²x³ – 16x⁵y⁵ = 8x³y²(x³ + 3 - 2x²y³).

12.  (x – 3)(3x + 1) + (3 – x)(3 + x) =  (x – 3)(3x + 1) – (x – 3)(3 + x) =

      = (x – 3)(3x + 1 – 3 – x) =  (x – 3)(2x – 2) = 2(x – 3)(x – 1).

13. a³(a + 6)² – 3a⁴(6 + a) = a³(a + 6)² – 3a⁴(a + 6) = a³(a + 6)(a + 6 – 3a) =

     = a³(a + 6)(–2a + 6) = –2a³(a + 6)(a – 3).