Maths Assignment: Simplifying Expressions and Substitution Practice

This mathematics assignment, designed for students, covers a range of algebraic concepts. Part 1 focuses on multiplying, dividing, and using brackets with algebraic terms. Part 2 continues with multiplication, division, and expanding expressions. Part 3 delves into adding and subtracting expressions, simplifying them by combining like terms. Part 4 provides further practice in adding and subtracting terms. Part 5 explores substitution, where values are assigned to variables. Part 6 focuses on substitution within tables of values and graphing. The assignment covers perimeter calculations, and the problems involve various algebraic manipulations to test and reinforce understanding of fundamental mathematical principles.

Mathematics Assignment
Student Name
Institution Name
Date of submission

Part 1: Multiplying, dividing and using brackets
Multiply
1. 2 h∗3 u=6 hu
2. 4 r∗3 f =12 rf
3. 10 k∗3 k=30 k2
4. 4 c∗2 c=8 c2
5. 7 md∗2 d=14 md2
6. 3 e∗2 d∗5=30 de
7. 8 y∗2 x∗3 y =48 x y2
8. 4 de∗3 ed∗2=24 d2 e2
9. 5 b∗3 c∗bc=15 b2 c2
10. ac∗a∗c∗b=a2 c2 b
11. 2 t∗utx∗u=2 t2 u2 x
12. d∗2 d∗u=2d2 u
13. cn∗nc∗ab=c2 n2 ab
14. 4 v∗2 w∗5 u=40 vwu
15. abc∗abc=a2 b2 c2
16. 2 abc∗2 cba=4 a2 b2 c2
17. 9 k∗2 ek∗u=18 k2 eu
18. 2 y∗3 d∗dy=6 y2 d2
19. 5 fn∗3∗fe=15 f 2 ne
20. abc∗bcd=a b2 c2 d
Divide
21. 3u
2 =3
2 u
22. 15 x
3 =5 x
23. 20 k
6 =10
3 k
24. 8 bc
3 b = 8
3 c

25. 9 ch
3 h =3 c
26. 14 ed
4 d =7
2 e
27. 4 g2
2 g =2 g
28. 15 b2
5 b2 =3
29. 6 c k2
2 k =3 ck
30. 16 d2
6 d = 8
3 d
31. 9 a b2
6 ab = 3
2 b
32. a2 b2
a b2 =a
Finding area
33. Square
A=l4
A= ( 2 a )2=4 a2
34. Rectangle
A=¿lb
A= ( 4 y∗2u ) =8 yu
35. Rectangle
A=lb
A=5 ef∗9 f =45 f 2 e
36. Triangle
A=1
2 bh
A=1
2∗ ( eb∗4 ea )=2 e2 ba
37. Triangle
A=1
2∗bh= 1
2∗6 bcd∗4 abc=12 b2 c2 ad

Part 2: Multiplying, dividing and using brackets
Multiply
1. 2∗a=2a
2. c∗3=3 c
3. 4∗e∗2=8 e
4. 2∗f ∗5=10 f
5. 3∗4∗u=12u
6. 8∗h∗2=16 h
7. 3∗x∗y=3 xy
8. 7∗t∗k =7 tk
9. g∗2∗g=2 g2
10. a∗b∗c=abc
11. q∗u∗q∗7=7 q2 u
12. n∗5∗3∗n=15 n2
13. x∗4∗t=4 xt
14. 10∗z∗q=10 qz
15. h∗3∗b∗4=12 bh
16. 6∗n∗n∗b=6 n2 b
17. e∗e∗t∗t=e2 t2
18. d∗a∗d∗3=3 a d2
19. 9∗6∗t∗t=54 t2
20. v∗v∗3∗y=3 v2 y
Divide
21. c
7 = 1
7 c
22. 2∗g
3 = 2
3 g
23. 15∗k
3 =5 k
24. 22∗e
4 =11
2 e

25. 7∗b
7 =b
26. 4∗f
8 =1
2 f
27. 18∗a
6 =3 a
28. 45∗y
9 =5 y
29. 50 d
10 =5 d
30. 9 e
6 = 3
2 e
31. 35 y
10 = 7
2 y
32. 48 a
3 =16 a
Expand
33. 4 ( c +6 ) =4 c +24
34. 6 ( m+3 )=6 m+18
35. 5 ( c−8 )=5 c−40
36. 7 ( 3 d +2 )=21 d +14
37. h ( h+2 ) =h2 +2 h
38. e ( k +e )=ke +e2
39. 5 n ( n−11 )=5 n2−55
40. 3 x ( x−3 )=3 x2−9 x
41. k ( m+d )=km+ kd
42. 3 w ( a+2 )=3 wa+6 w
43. 2 q ( 3 q−2 )=6 q2−4 q
44. 8 e ( 7e+3 ) =56 e2+24 e
45. 2 m ( e +2 m )=2 me+4 m2
46. 9 w ( w−4 )=9 w2−36 w
47. a2 ( b+ c )=a2 b+ a2 c
48. x2 ( d2+t2 )=x2 d2+ x2 t2

49. 3 u ( 2−t2 ) =6 u−3 u t2
Part 3: Adding and Subtracting
1. 3 a+5 t +3−a+6+ 4 t
3 a−a+5 t +4 t +3+6
¿ 2 a+9 t +9
2. 12 d+ 2 a+16−5 d−7+3 a
12 d−5 d +2 a+3 a+16−7
¿ 7 d +5 a+9
3. 4 ux+3 xa−3 xu+2 ax
4 ux−3 xu+3 xa+2 ax
¿ ux +5 xa
4. 5+5 m+21−4 m+3 ma
5+21+5 m−4 m+3 ma
¿ 26+ m+3 ma
5. 12 kd−5 dk −5 dk−8−kd
12 kd−5 dk −5 dk−kd−8
¿ kd −8
6. 5+a+ b+6+ 2ab +3 b
5+6+ a+b+ 3 b+2 ab
¿ 11+a+ 4 b+ 2ab
7. 5 tu+17 +12ut−12 t−12
5 tu+12 ut+17−12−12t
¿ 17 tu+ 5−12 t
8. 20 a−20−a+5 ta+11 at
20 a−a−20+5 ta+11 at
¿ 19 a−20+16 at
9. 30 ue+15e-5e−u
30 ue+10e−u
10. at +ta+ at+ ta+a−4 t

4 at + a−4 t
11. 17+20 as−3−15 sa−3 as
17−3+20 as−15 sa−3 as
¿ 14+ 2as
12. 17+2 m2−m+m2+ 14
17+14 +2 m2 +m2−m
31+3 m2−m
13. 7 h2 +3 h−3 h2+ 4−4 h2
7 h2−3 h2−4 h2 +3 h+4
3 h+ 4
14. 20 k2 +14−12 k−8 k2−7
20 k2−8 k2 +14−7−12 k
12 k2 +7−12k
15. 9 r2−5 tr +7−3 r2+16−2 rt
9 r2−3r 2−5 tr−2rt +16
6 r2−7 tr+16
16. 13e+5 e2−8e-2 e2−5−4 e
13e-8e-4e+5 e2 −2 e2−5
e +3 e2−5
17. 20 cw+37−c2 −18 wc−19
20 cw−18 wc+37−19−c2
¿ 2 cw+18−c2
18. 9 f g2 +3 f 2 g+3 g2 f
¿ 9 f g2 +3 g2 f +3 f 2 g
¿ 12 f g2 +3 f 2 g
19. 10 y t2 +3 y2 t +5 y t2
10 y t2 +5 y t2 +3 y2 t
¿ 15 y t2 +3 y2 t
20. 5 a2 +3 a2 t −3 a2 −2t a2
5 a2 −3 a2 +3 a2 t−2t a2
2 a2 +t a2

21. y2 +2 x y2 +3 y2− y2 x2
y2 +3 y2+ 2 x y2− y2 x2
¿ 4 y2+ 2 x y2− y2 x2
Expression for the perimeter
22. All sides are equal
p=3 ( ha+ 4 )=3 ha+12
23. P=4 ( 2 ed ) +2 ( de+6 )
8 ed +2 de+12=10 de+12
24. P=2 ( 6 x ) +2 x + ( 6 x−x ) +(6 x−2 x )
12 x+2 x+ 6 x−x+ 6 x−2 x=23 x
Part 4: Adding and Subtracting
1. t+ t=2t
2. k + 2k =3 k
3. 6 m−4 m=2 m
4. 12 i+3 i=15 i
5. 2 j+5 j=7 j
6. 16e-9 e=7 e
7. 9 x +5 x+3 x=17 x
8. 12 b+9 b+4 b=25 b
9. 6 n+2 n+n=9 n
10. t+ 6 t−2t =5 t
11. 3e+5e-4 e=4 e
12. 12 r−7 r +2 r =7 r
13. 11 k−7 k−4 k =0
14. 24 h−9 h−14 h=h
15. 2 c+ 5 c+7 c=14 c
16. u+5 u−2u=4 u
17. 6 d −3 d−2 d=d
18. 14 q−11 q−3 q=0

19. 8 v−2 v−3 v=3 v
20. 12 s+ 3 s−14 s=s
21. a+ g+ a=2 a+g
22. 2e+ c+ e=3e+c
23. 4 h+3 h+2 d=7 h+ 2d
24. 10 m−3 n−m=9 m−3 n
25. 2 c−7 q+ 3 c=5 c−7 q
26. 9 k +3 k +n=12 k + n
27. 3e+2 f −f =3e+f
28. m+ p−m=p
29. 4 d−2 m+d=5 d−2m
30. 6 m+3 b−5 m=m+3 b
31. 2 d +3 d−h=5 d−h
32. t+ 5e−t=5 e
33. 5e-2e+q=3e+q
34. 3 a−2 d−2 a=a−2 d
35. 4 c +2b−b=4 c +b
36. 6 w +n−6 w=n
37. 6 n−3 n+2 d=3 n+2 d
38. 2 f +3 f +f −2 d=6 f −2 d
39. a+b+a+ b=2 a+ 2b
40. d +3 d +3 e=4 d +3 e
41. 2 a+3+2 a=4 a+3
42. 5e+4−4 e=e +4
43. 10 d−3 d −6=7 d−6
44. 3+ 4 q+2−q=5+3 q
45. 4 y +12−3 y= y +12
46. 4 k +2+5−k=3 k +7
47. a+2+ 2a−1=3 a+1
48. 2 d−5+4 d=6 d−5
49. 5+3e-2+e=3+4 e
50. t+ 4−t−2=2

51. 3 v −6−2 v=v−6
52. 10+2 b−5=5+2 b
53. a+ 8−a+8=16
54. 6 x−10+ 4 x=10 x−10
55. 9 m+6−8 m=m+6
56. 5+b−4+b=1+2 b
57. 2 f −10−f =f −10
58. 10+k + 15=25+ k
59. h+3+ h+1=2 h+ 4
60. y +2 y−3+ y =4 y −3
Part 5: Substitution
The value of a=4
1. b=a+3
¿ 4 +3=7
2. h=a+8
¿ 4 +8=12
3. m=2 a−2
¿ ( 2∗4 ) −2=6
4. w=6 a−5
¿ ( 6∗4 ) −5=19
5. q=5 a+7
¿ ( 5∗4 ) +7=27
6. u=11a−23
¿ ( 11∗4 )−23=21
7. k =11 a−10
¿ ( 11∗4 )−10=34
8. t=k 2+3
¿ 52 +3=28
9. g=e2 −5

¿ 72−5=44
10. m=k2−k
¿ 52−5=20
11. e2 −4
9 =72−4
9
¿ 5
12. ¿ 8 k2
4 = 8∗52
4 =50
13. b=100−e2
¿ 100−72=51
14. r =2 k2=2∗52=50
15. v=2 ( m+7 )
¿ 2(10+7)
¿ 2 ( 17 )=34
16. c=9(f +5)
¿ 9(4+ 5)
¿ 9 ( 9 )=81
17. x=f (m−3)
¿ 4 (10−3)
¿ 4 ( 7 )=28
18. g=f ( m−f )
¿ 4 (10−4)
¿ 4 ( 6 ) =24
19. n=7(20−m)
¿ 7(20−10)
¿ 7 ( 10 )=70
20. q=m(m−2 f )
¿ 10(10−2∗4)
¿ 10(10−8)
¿ 10 ( 2 )=20
21. t= 2 m
f +1

¿ 2∗10
4 +1 = 20
5 =4
Part 6: Substitution (Tables of Values)
1. Rule; c=2k
k 0 1 2 3 4
c 0 2 4 6 8
¿ 2∗0=0
¿ 2∗1=2
¿ 2∗2=4
¿ 2∗3=6
¿ 2∗4=8
2. Rule; m=3 t +1
t 0 5 10 15 20
m 1 16 31 46 61
¿ ( 3∗0 ) +1=1
¿ ( 3∗5 ) +1=16
¿ ( 3∗10 ) +1=31
¿ ( 3∗15 ) +1=46
¿ ( 3∗20 ) +1=61
3. Rule: d=3e-2
e 2 4 6 8 10
d 4 10 16 22 28
¿ ( 3∗2 )−2=4
¿ ( 3∗4 )−2=10
¿ ( 3∗6 ) −2=16
¿ ( 3∗8 )−2=22
¿ ( 3∗10 )−2=28