Разложите многочлен на множители:

1) ax+ay+bx+by

2) ax-ay+bx-by

3) a^2 + ab+ac+bc

4) ax+ay+6x+6y

5) 1-bx-x+b

6) ab+2b-2a-4

7) x^2 + xy+ax+ay

8) am-an+m-n

9) 3x-3y+ax-ay

10) ab-a^2 + 2a-2b

1)

ax+ay+bx+by = (ax+ay) + (bx+by) = a (x+y) + b (x+y) = (a+b) (x+y)

2)

ax-ay+bx-by = (ax-ay) + (bx-by) = a (x-y) + b (x-y) = (a+b) (x-y)

3)

a^2+ab+ac+bc = (a^2+ac) + (ab+bc) = a (a+c) + b (a+c) = (a+b) (a+c)

4)

ax+ay+6x+6y = (ax+ay) + (6x+6y) = a (x+y) + 6 (x+y) = (a+6) (x+y)

5)

1-bx-x+b = (1-x) - (bx-b) = (1-x) + b (1-x) = b (1-x) ^2

6)

ab+2b-2a-4 = (ab+2b) - (2a+4) = b (a+2) - 2 (a+2) = (b-2) (a+2)

1. a (x+y) + b (x+y)

2. a (x-y) + b (x-y)

3. a (a+b) + c (a+b)

4. a (x+y) + 6 (x+y)

5.-b (x-b) - 1 (x-b)

6. b (a+2) - 2 (a+2)

7. x (x+y) + a (x+y)

8. a (m-n) + m-n

9.3 (x-y) + a (x-y)

10. a (b-a) + 2 (a-b)