This document contains examples of algebraic expressions and equations. It shows how to combine like terms, factor expressions, and solve simple equations. For example, it shows that (x + 2)(x + 3) can be factored as x^2 + 5x + 6. It also provides step-by-step workings for subtracting expressions like 2y - (-5y) = 2y + 5y = 7y.

2. 1. . .
15 . 2/1
2. . .
17 . 2/1
3. . .
23 . 2/1
4. . .
26 . 2/1
5. . .
28 . 2/1

4. 9
“
”

5. a,
b, c, … ,x, y, z
5a 5a
5b 5c …
5x 5y
5z “
”

6. 1.
5
x 5
5 x (5)
x 5(x) 5x
2. 6

7. 3. 3
3x x
3 (3)
3( ) 3
4.

8. 3 , 5x , 7+2x

12. () 1
++,-- 2
*/% 3
+- 4

13. 1 (10 -34) * 5 =
10 - 3 = 7 5
35
35
2 5 + 10 *2 = 25 10 * 2 = 20 5
25
3 (2 + 7) * 4 % 10
2+7=9 4 36
=6
10 6
4 2 + 7 * 4 % 10 =
7 * 4 = 28
10
10 8 2 10
5 10 + 2 * 8 / 4 *
3 – 5 = 17 1. 2 * 8 = 16
2. 16 / 4 = 4
3. 4 * 3 = 12
4. 12 + 10 = 22

14. X Y,32 B,
3 -A
a 23,7
bc
X3 ,n+ ,
-Y 6
2/b
a3

16. 1.
3X
3xX 3.X
6+X

17. 2.

18. - X Y
Z
-
Xn X
n

19. -x2y3 = (-1)
x2 y3

20. -x2y3
x y -1
-
x2y3
2+3 5
-
x2y3

21. 1
-
2
1= 1) ×
-
2(- 2x0
= 1) ×
(- 2y0
)×
= 1x 0
(- 2×
y0

22. 0
0 = (0) × xn
n
= (0)
xn

23. 3xy, 4xy
xy
3xy 4xy

24. -
. x x
x + 18x =
(13+18)x
= 31x
2. 4xy xy
xy+8xy =

25. 3.
4.

26. 1. 3x2 + 4x2 = (3+ 4)
x2 = 7x2
2. 6x2 y + 8x2 y = (6
+ 8) x2 y =14x2 y
3. 3s3t2 + 5s3t2 =
(3+ 5) s3t2 = 8s3t2

27. 4. 2x − 4x = 2x + (−4) x
= (2 + (−4)) x = (2 − 4)
x = −2x
5. 15x2 y −8x2 y = (15
−8) x2 y = 7x2 y

28. xy

29. • x
+ (-3x)
x + (-3x) =[1
+ (-3) ] x
= (-2) x
= -2x
• -

31. -
-

32. a -b = a+(-b) a,b
-b
b

33. •
8x 3x
8x
8x – 3x
= 8x + (-3x)
=
[8 + (-3)]x
=

35. 3st -10st
3 st -
10st = 3st + (-
10st)
=
[3+(-10)]st
=

36. 2y – (-5y)
2y – (-
5y) = 2y + 5y
= (2 +5) y
= 7y

37. -
-
-

39. • (1) 2x
-3x + 4
1) 2x ( -
3x + 4)
= (2x)(-3x) +
(2x) (4)
= -6 x 2 + 8x

40. • -7x 2
8x 2 + 4x -5
-7x 2 ( 8x 2 +
4x -5)
= (-7x 2 )(8x 2 )
+
(-7x 2 )(4x) + (-
7x 2 ) (-5)

46. 1

47. 2

48. -

50. -

51. -

52. -

53. (x + 2)(x + 3) = (x + 2)(x)
+ (x+2)(3)
= x(x) + 2(x) + 3(x) +
2(3)
= x 2 + 2x + 3x + 6
= x 2 + 5x + 6

54. 1.

55. 2.

56. 3.

59. 4x