Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 152 · 40 sums

The method (Split into easy parts): (a + b)² = a² + 2ab + b². (a − b)² = a² − 2ab + b². (a + b)(a − b) = a² − b²; so a² − b² = (a + b)(a − b). a² + b² = (a + b)² − 2ab = (a − b)² + 2ab.

1. 1.Find the value of x² + 2xy + y² when x = 3 and y = 1.
2. 2.Find the value of x² + 2xy + y² when x = 10 and y = 7.
3. 3.If a − b = 1 and ab = 30, what is a² + b²?
4. 4.If a − b = 1 and ab = 42, what is a² + b²?
5. 5.If a + b = 3 and ab = 2, what is a² + b²?
6. 6.If a + b = 5 and ab = 4, what is a² + b²?
7. 7.If a + b = 9 and ab = 20, what is a² + b²?
8. 8.Find the value of x² − y² when x = 8 and y = 7.
9. 9.Use (a − b)² = a² − 2ab + b² to find 27².
10. 10.Use a² − b² = (a + b)(a − b) to find 58² − 14².
11. 11.Use (a + b)² = a² + 2ab + b² to find 53².
12. 12.Use (a + b)² = a² + 2ab + b² to find 47².
13. 13.Find the value of x² − y² when x = 10 and y = 3.
14. 14.Use a² − b² = (a + b)(a − b) to find 25² − 2².
15. 15.Use (a + b)² = a² + 2ab + b² to find 38².
16. 16.Find the value of x² − 2xy + y² when x = 9 and y = 2.
17. 17.Use (a + b)² = a² + 2ab + b² to find 98².
18. 18.If a + b = 14 and ab = 33, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 55².
20. 20.Use (a + b)² = a² + 2ab + b² to find 14².
21. 21.Use a² − b² = (a + b)(a − b) to find 53² − 52².
22. 22.Use (a + b)² = a² + 2ab + b² to find 54².
23. 23.Use a² − b² = (a + b)(a − b) to find 65² − 14².
24. 24.If a + b = 7 and ab = 12, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 47².
26. 26.Use (a + b)² = a² + 2ab + b² to find 25².
27. 27.Use (a + b)(a − b) = a² − b² to find 97 × 83.
28. 28.Use (a + b)(a − b) = a² − b² to find 102 × 98.
29. 29.Find the value of x² − y² when x = 7 and y = 6.
30. 30.Use (a + b)(a − b) = a² − b² to find 36 × 24.
31. 31.Use (a + b)(a − b) = a² − b² to find 104 × 96.
32. 32.Find the value of x² + 2xy + y² when x = 5 and y = 3.
33. 33.Find the value of x² − y² when x = 12 and y = 8.
34. 34.If a − b = 3 and ab = 10, what is a² + b²?
35. 35.Use (a − b)² = a² − 2ab + b² to find 69².
36. 36.Use (a + b)² = a² + 2ab + b² to find 105².
37. 37.Use (a − b)² = a² − 2ab + b² to find 74².
38. 38.Use (a − b)² = a² − 2ab + b² to find 19².
39. 39.Use (a + b)² = a² + 2ab + b² to find 108².
40. 40.Find the value of x² + 2xy + y² when x = 13 and y = 10.

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