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Page 1
Algebraic Expressions and Identities
Points to Remember
Standard Algebraic Identities
? (?? + ?? )
?? = ?? ?? + ?? ???? + ?? ??
? (?? - ?? )
?? = ?? ?? - ?? ???? + ?? ??
? (?? + ?? )
?? = (?? - ?? )
?? + ?? ????
? (?? - ?? )
?? = (?? + ?? )
?? - ?? ????
? (?? + ?? )(?? - ?? ) = ?? ?? - ?? ??
? (?? + ?? )(?? + ?? ) = ?? ?? + (?? + ?? )?? + ????
? (?? - ?? )(?? + ?? ) = ?? ?? + (-?? + ?? )?? - ????
? (?? + ?? )(?? - ?? ) = ?? ?? + (?? - ?? )?? - ????
? (?? - ?? )(?? - ?? ) = ?? ?? - (?? + ?? )?? + ????
? (?? + ?? )
?? = ?? ?? + ?? ?? + ?????? (?? + ?? )
? (?? - ?? )
?? = ?? ?? - ?? ?? - ?????? (?? - ?? )
? ?? ?? - ?? ?? = (?? - ?? )(?? ?? + ???? + ?? ?? )
? ?? ?? + ?? ?? = (?? + ?? )(?? ?? - ???? + ?? ?? )
QUESTIONS
1. Simplify: (?? ?? ?? - ???? ?? ?? )
??
2. Simplify: (???? ?? ?? - ???? ?? ?? ) ÷ (???? + ???? )
3. Simplify: (???? + ???? )(???? - ???? ) - ?? ?? ??
4. Simplify: (???? - ???? )
?? + ????????
5. Simplify:
?? ?? ?? +???????? +???? ?? ?? ???? +????
6. Simplify: (?? ?? + ???? + ?? ) ÷ (?? + ?? )
7. Simplify: (?? . ???? ?? ?? - ?? . ???? ?? ?? ) ÷ (?? . ???? + ?? . ???? )
8. Simplify: (???? + ???? )
?? - ???? ?? ?? - ???? ?? ??
9. Simplify: (?? ?? + ?????? + ???? ) ÷ (?? + ?? )
Page 2
Algebraic Expressions and Identities
Points to Remember
Standard Algebraic Identities
? (?? + ?? )
?? = ?? ?? + ?? ???? + ?? ??
? (?? - ?? )
?? = ?? ?? - ?? ???? + ?? ??
? (?? + ?? )
?? = (?? - ?? )
?? + ?? ????
? (?? - ?? )
?? = (?? + ?? )
?? - ?? ????
? (?? + ?? )(?? - ?? ) = ?? ?? - ?? ??
? (?? + ?? )(?? + ?? ) = ?? ?? + (?? + ?? )?? + ????
? (?? - ?? )(?? + ?? ) = ?? ?? + (-?? + ?? )?? - ????
? (?? + ?? )(?? - ?? ) = ?? ?? + (?? - ?? )?? - ????
? (?? - ?? )(?? - ?? ) = ?? ?? - (?? + ?? )?? + ????
? (?? + ?? )
?? = ?? ?? + ?? ?? + ?????? (?? + ?? )
? (?? - ?? )
?? = ?? ?? - ?? ?? - ?????? (?? - ?? )
? ?? ?? - ?? ?? = (?? - ?? )(?? ?? + ???? + ?? ?? )
? ?? ?? + ?? ?? = (?? + ?? )(?? ?? - ???? + ?? ?? )
QUESTIONS
1. Simplify: (?? ?? ?? - ???? ?? ?? )
??
2. Simplify: (???? ?? ?? - ???? ?? ?? ) ÷ (???? + ???? )
3. Simplify: (???? + ???? )(???? - ???? ) - ?? ?? ??
4. Simplify: (???? - ???? )
?? + ????????
5. Simplify:
?? ?? ?? +???????? +???? ?? ?? ???? +????
6. Simplify: (?? ?? + ???? + ?? ) ÷ (?? + ?? )
7. Simplify: (?? . ???? ?? ?? - ?? . ???? ?? ?? ) ÷ (?? . ???? + ?? . ???? )
8. Simplify: (???? + ???? )
?? - ???? ?? ?? - ???? ?? ??
9. Simplify: (?? ?? + ?????? + ???? ) ÷ (?? + ?? )
10. Simplify: (?? + ?? )(?? ?? + ?? ?? - ???? )
11. Simplify: (?? ?? + ???? + ?? ?? )(?? - ?? )
12. If ?? = ?? , ?? = ?? , then find the value of (?? + ?? )
?? + ????
13. If ?? = -?? , ?? = ?? , ?? = ?? , ?? = ?? , then find the value of (?? - ?? )
?? + (?? + ?? )
??
14. If ?? = ?? , ?? = -?? then find the value of (?? + ?? )
?? - ????
15. If ?? = ???? , ?? = ???? then find the value of (?? - ?? )
?? + (?? + ?? )
16. If ?? = ?? . ?? , ?? = ?? . ?? then find the value of (?? + ?? )
?? - (?? )
??
17. If ?? = ???? , ?? = -?? , ?? = ?? , then find the value of (?? + ?? + ?? )
??
18. If ?? =
??????
v???? +(?? ?? ×?? )
then find the value of ?? ??
19. If ?? = ??????
?? - ??????
?? then find the value of ?? - ??
20. If ?? = ??????
?? - ????
?? then find the value of ?? + ??
21. If ?? = ?????? , ?? = ???? then find the value of (?? - ?? )
?? + (?? + ?? )
22. Simplify: (v???? - v ???? )(v ???? - v ?? ) + v ???? - v ????
23. Simplify: (???? - ?? )
?? - (?? + ???? )
?? + ?? ?? ?? + ????
24. Simplify: (?? + ?? )
?? + (?? - ?? )
?? - ????
25. Simplify: (?? - ?? )(?? + ?? ) + (?? + ?? )(?? - ?? ) + ?? ?? - ?? ??
26. If (?? )
?? - (?? . ?? )
?? = ?? , find the value of (?? . ???? × ?? )
27. If (?? + ?? )
?? = ?? + ?? v ?? , then find the value of a and b.
28. Simplify: (?? + ?? )
?? - (?? - ?? )
?? + ?? - ??
29. What should be subtracted from (?? + ?? )
?? to make it (?? - ?? )
?? ?
30. What should be added in ??????
?? + ???? ?? ?? to make it (???? + ???? )
?? ?
31. ?????? ?? ?? - ?????? ?? ?? should be divided by which expression to get ?????? + ?????? ?
32. Simplify: (???? + ???? )
?? + ????????
33. Simplify: (???? - ???? )
?? - ??????
??
34. Simplify: (?? . ???? - ?? . ???? )
?? + ?? . ?????? + ?? . ??????
35. What should be subtracted from (?? + ?? )
?? to get ?? ?? + ?? ?? ?
36. The sides of a rectangle are ???? units and ???? units. Find the area and perimeter
of the rectangle.
37. Find the value of ???? × ?? . ??
38. Find the value of ?????? × ??????
Page 3
Algebraic Expressions and Identities
Points to Remember
Standard Algebraic Identities
? (?? + ?? )
?? = ?? ?? + ?? ???? + ?? ??
? (?? - ?? )
?? = ?? ?? - ?? ???? + ?? ??
? (?? + ?? )
?? = (?? - ?? )
?? + ?? ????
? (?? - ?? )
?? = (?? + ?? )
?? - ?? ????
? (?? + ?? )(?? - ?? ) = ?? ?? - ?? ??
? (?? + ?? )(?? + ?? ) = ?? ?? + (?? + ?? )?? + ????
? (?? - ?? )(?? + ?? ) = ?? ?? + (-?? + ?? )?? - ????
? (?? + ?? )(?? - ?? ) = ?? ?? + (?? - ?? )?? - ????
? (?? - ?? )(?? - ?? ) = ?? ?? - (?? + ?? )?? + ????
? (?? + ?? )
?? = ?? ?? + ?? ?? + ?????? (?? + ?? )
? (?? - ?? )
?? = ?? ?? - ?? ?? - ?????? (?? - ?? )
? ?? ?? - ?? ?? = (?? - ?? )(?? ?? + ???? + ?? ?? )
? ?? ?? + ?? ?? = (?? + ?? )(?? ?? - ???? + ?? ?? )
QUESTIONS
1. Simplify: (?? ?? ?? - ???? ?? ?? )
??
2. Simplify: (???? ?? ?? - ???? ?? ?? ) ÷ (???? + ???? )
3. Simplify: (???? + ???? )(???? - ???? ) - ?? ?? ??
4. Simplify: (???? - ???? )
?? + ????????
5. Simplify:
?? ?? ?? +???????? +???? ?? ?? ???? +????
6. Simplify: (?? ?? + ???? + ?? ) ÷ (?? + ?? )
7. Simplify: (?? . ???? ?? ?? - ?? . ???? ?? ?? ) ÷ (?? . ???? + ?? . ???? )
8. Simplify: (???? + ???? )
?? - ???? ?? ?? - ???? ?? ??
9. Simplify: (?? ?? + ?????? + ???? ) ÷ (?? + ?? )
10. Simplify: (?? + ?? )(?? ?? + ?? ?? - ???? )
11. Simplify: (?? ?? + ???? + ?? ?? )(?? - ?? )
12. If ?? = ?? , ?? = ?? , then find the value of (?? + ?? )
?? + ????
13. If ?? = -?? , ?? = ?? , ?? = ?? , ?? = ?? , then find the value of (?? - ?? )
?? + (?? + ?? )
??
14. If ?? = ?? , ?? = -?? then find the value of (?? + ?? )
?? - ????
15. If ?? = ???? , ?? = ???? then find the value of (?? - ?? )
?? + (?? + ?? )
16. If ?? = ?? . ?? , ?? = ?? . ?? then find the value of (?? + ?? )
?? - (?? )
??
17. If ?? = ???? , ?? = -?? , ?? = ?? , then find the value of (?? + ?? + ?? )
??
18. If ?? =
??????
v???? +(?? ?? ×?? )
then find the value of ?? ??
19. If ?? = ??????
?? - ??????
?? then find the value of ?? - ??
20. If ?? = ??????
?? - ????
?? then find the value of ?? + ??
21. If ?? = ?????? , ?? = ???? then find the value of (?? - ?? )
?? + (?? + ?? )
22. Simplify: (v???? - v ???? )(v ???? - v ?? ) + v ???? - v ????
23. Simplify: (???? - ?? )
?? - (?? + ???? )
?? + ?? ?? ?? + ????
24. Simplify: (?? + ?? )
?? + (?? - ?? )
?? - ????
25. Simplify: (?? - ?? )(?? + ?? ) + (?? + ?? )(?? - ?? ) + ?? ?? - ?? ??
26. If (?? )
?? - (?? . ?? )
?? = ?? , find the value of (?? . ???? × ?? )
27. If (?? + ?? )
?? = ?? + ?? v ?? , then find the value of a and b.
28. Simplify: (?? + ?? )
?? - (?? - ?? )
?? + ?? - ??
29. What should be subtracted from (?? + ?? )
?? to make it (?? - ?? )
?? ?
30. What should be added in ??????
?? + ???? ?? ?? to make it (???? + ???? )
?? ?
31. ?????? ?? ?? - ?????? ?? ?? should be divided by which expression to get ?????? + ?????? ?
32. Simplify: (???? + ???? )
?? + ????????
33. Simplify: (???? - ???? )
?? - ??????
??
34. Simplify: (?? . ???? - ?? . ???? )
?? + ?? . ?????? + ?? . ??????
35. What should be subtracted from (?? + ?? )
?? to get ?? ?? + ?? ?? ?
36. The sides of a rectangle are ???? units and ???? units. Find the area and perimeter
of the rectangle.
37. Find the value of ???? × ?? . ??
38. Find the value of ?????? × ??????
39. If ?? = ?? + v ?? and ?? = ?? - v ?? , then find the value of (?? - ?? )
?? .
40. Find the square root of ?? + ?? v ?? .
41. Find the square root of ???? - ?? v?? .
42. If (???? )
?? = (???? )
?? + ???? , then find the value of ?? .
43. If ?? = ?? . ?? and ?? = ?? . ?? , then find the value of ?? ?? + ?? ?? + ???? .
44. If ?? = ?? and ?? = ?? . ?? , then find the value of ?? ?? + ?? ?? - ???? .
45. If x= ?? + ?? v ?? and ?? = ???? + ???? v ?? , then find the value of v?? - v ?? .
Page 4
Algebraic Expressions and Identities
Points to Remember
Standard Algebraic Identities
? (?? + ?? )
?? = ?? ?? + ?? ???? + ?? ??
? (?? - ?? )
?? = ?? ?? - ?? ???? + ?? ??
? (?? + ?? )
?? = (?? - ?? )
?? + ?? ????
? (?? - ?? )
?? = (?? + ?? )
?? - ?? ????
? (?? + ?? )(?? - ?? ) = ?? ?? - ?? ??
? (?? + ?? )(?? + ?? ) = ?? ?? + (?? + ?? )?? + ????
? (?? - ?? )(?? + ?? ) = ?? ?? + (-?? + ?? )?? - ????
? (?? + ?? )(?? - ?? ) = ?? ?? + (?? - ?? )?? - ????
? (?? - ?? )(?? - ?? ) = ?? ?? - (?? + ?? )?? + ????
? (?? + ?? )
?? = ?? ?? + ?? ?? + ?????? (?? + ?? )
? (?? - ?? )
?? = ?? ?? - ?? ?? - ?????? (?? - ?? )
? ?? ?? - ?? ?? = (?? - ?? )(?? ?? + ???? + ?? ?? )
? ?? ?? + ?? ?? = (?? + ?? )(?? ?? - ???? + ?? ?? )
QUESTIONS
1. Simplify: (?? ?? ?? - ???? ?? ?? )
??
2. Simplify: (???? ?? ?? - ???? ?? ?? ) ÷ (???? + ???? )
3. Simplify: (???? + ???? )(???? - ???? ) - ?? ?? ??
4. Simplify: (???? - ???? )
?? + ????????
5. Simplify:
?? ?? ?? +???????? +???? ?? ?? ???? +????
6. Simplify: (?? ?? + ???? + ?? ) ÷ (?? + ?? )
7. Simplify: (?? . ???? ?? ?? - ?? . ???? ?? ?? ) ÷ (?? . ???? + ?? . ???? )
8. Simplify: (???? + ???? )
?? - ???? ?? ?? - ???? ?? ??
9. Simplify: (?? ?? + ?????? + ???? ) ÷ (?? + ?? )
10. Simplify: (?? + ?? )(?? ?? + ?? ?? - ???? )
11. Simplify: (?? ?? + ???? + ?? ?? )(?? - ?? )
12. If ?? = ?? , ?? = ?? , then find the value of (?? + ?? )
?? + ????
13. If ?? = -?? , ?? = ?? , ?? = ?? , ?? = ?? , then find the value of (?? - ?? )
?? + (?? + ?? )
??
14. If ?? = ?? , ?? = -?? then find the value of (?? + ?? )
?? - ????
15. If ?? = ???? , ?? = ???? then find the value of (?? - ?? )
?? + (?? + ?? )
16. If ?? = ?? . ?? , ?? = ?? . ?? then find the value of (?? + ?? )
?? - (?? )
??
17. If ?? = ???? , ?? = -?? , ?? = ?? , then find the value of (?? + ?? + ?? )
??
18. If ?? =
??????
v???? +(?? ?? ×?? )
then find the value of ?? ??
19. If ?? = ??????
?? - ??????
?? then find the value of ?? - ??
20. If ?? = ??????
?? - ????
?? then find the value of ?? + ??
21. If ?? = ?????? , ?? = ???? then find the value of (?? - ?? )
?? + (?? + ?? )
22. Simplify: (v???? - v ???? )(v ???? - v ?? ) + v ???? - v ????
23. Simplify: (???? - ?? )
?? - (?? + ???? )
?? + ?? ?? ?? + ????
24. Simplify: (?? + ?? )
?? + (?? - ?? )
?? - ????
25. Simplify: (?? - ?? )(?? + ?? ) + (?? + ?? )(?? - ?? ) + ?? ?? - ?? ??
26. If (?? )
?? - (?? . ?? )
?? = ?? , find the value of (?? . ???? × ?? )
27. If (?? + ?? )
?? = ?? + ?? v ?? , then find the value of a and b.
28. Simplify: (?? + ?? )
?? - (?? - ?? )
?? + ?? - ??
29. What should be subtracted from (?? + ?? )
?? to make it (?? - ?? )
?? ?
30. What should be added in ??????
?? + ???? ?? ?? to make it (???? + ???? )
?? ?
31. ?????? ?? ?? - ?????? ?? ?? should be divided by which expression to get ?????? + ?????? ?
32. Simplify: (???? + ???? )
?? + ????????
33. Simplify: (???? - ???? )
?? - ??????
??
34. Simplify: (?? . ???? - ?? . ???? )
?? + ?? . ?????? + ?? . ??????
35. What should be subtracted from (?? + ?? )
?? to get ?? ?? + ?? ?? ?
36. The sides of a rectangle are ???? units and ???? units. Find the area and perimeter
of the rectangle.
37. Find the value of ???? × ?? . ??
38. Find the value of ?????? × ??????
39. If ?? = ?? + v ?? and ?? = ?? - v ?? , then find the value of (?? - ?? )
?? .
40. Find the square root of ?? + ?? v ?? .
41. Find the square root of ???? - ?? v?? .
42. If (???? )
?? = (???? )
?? + ???? , then find the value of ?? .
43. If ?? = ?? . ?? and ?? = ?? . ?? , then find the value of ?? ?? + ?? ?? + ???? .
44. If ?? = ?? and ?? = ?? . ?? , then find the value of ?? ?? + ?? ?? - ???? .
45. If x= ?? + ?? v ?? and ?? = ???? + ???? v ?? , then find the value of v?? - v ?? .
ANSWERS
Question No. Answer Question No. Answer
1.
?? ?? ?? + ?? ?? ?? ?? ?? - ???? ?? ?? ?? ?? 24. ?? ?? ?? + ?? ?? ?? - ????
2.
5x-4y 25. ?? ?? ?? - ?? ?? ??
3.
?? ?? ?? - ?? ?? ?? 26. ?? = ?? . ????????
4.
16?? ?? + ?? ?? ?? 27.
?? = v?? , ?? = v?? ????
?? = v?? , ?? = v??
5.
???? + ???? 28. ?????? + ?? - ??
6.
?? + ?? 29. ??????
7.
?? . ???? - ?? . ???? 30. ????????
8.
???????? 31. ?????? - ??????
9.
?? + ?? 32. ?? ?? ?? + ?? ?? ?? + ????????
10.
?? ?? + ?? ?? 33. ?? ?? ?? - ????????
11.
?? ?? - ?? ?? 34.
?? . ???? ?? ?? + ?? . ???? ?? ?? + ?? . ??????
12.
???? 35. ??????
13.
4 36.
Area=???????? sq.units,
Perimeter=(?????? + ?????? )
units
14.
39 37. 359.9
15.
76 38. 89996
16.
-4 39. 12
17.
343 40.
v?? + v??
18.
400 41.
?? - v??
19.
200 42. ?? = ??????
20.
400 43. 1.29
21.
202 44. 19.24
22.
3 45.
?? + v??
23.
3?? ?? - ??????
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Document Description: Mental Maths Questions and Answers: Algebraic Expression and Identities for Class 8 2024 is part of Mental Mathematics for Class 8 preparation.
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