Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 984 · 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 = 10 and y = 4.
2. 2.Use (a − b)² = a² − 2ab + b² to find 32².
3. 3.If a − b = 3 and ab = 4, what is a² + b²?
4. 4.Use a² − b² = (a + b)(a − b) to find 58² − 3².
5. 5.Find the value of x² − y² when x = 14 and y = 2.
6. 6.Find the value of x² − 2xy + y² when x = 4 and y = 1.
7. 7.Use (a + b)² = a² + 2ab + b² to find 107².
8. 8.Use (a + b)² = a² + 2ab + b² to find 85².
9. 9.Find the value of x² − y² when x = 7 and y = 6.
10. 10.Use (a − b)² = a² − 2ab + b² to find 63².
11. 11.Use a² − b² = (a + b)(a − b) to find 43² − 39².
12. 12.Use (a + b)² = a² + 2ab + b² to find 96².
13. 13.Use (a + b)(a − b) = a² − b² to find 27 × 13.
14. 14.Find the value of x² − y² when x = 9 and y = 8.
15. 15.Use (a + b)² = a² + 2ab + b² to find 17².
16. 16.Use a² − b² = (a + b)(a − b) to find 69² − 17².
17. 17.Find the value of x² − 2xy + y² when x = 14 and y = 7.
18. 18.Use a² − b² = (a + b)(a − b) to find 82² − 45².
19. 19.Use (a + b)² = a² + 2ab + b² to find 97².
20. 20.Use (a + b)² = a² + 2ab + b² to find 56².
21. 21.Find the value of x² + 2xy + y² when x = 13 and y = 7.
22. 22.Use (a + b)² = a² + 2ab + b² to find 58².
23. 23.Find the value of x² − y² when x = 12 and y = 7.
24. 24.Use a² − b² = (a + b)(a − b) to find 78² − 40².
25. 25.If a + b = 12 and ab = 20, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 103².
27. 27.If a + b = 13 and ab = 22, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 41².
29. 29.Use (a + b)(a − b) = a² − b² to find 36 × 24.
30. 30.Find the value of x² − 2xy + y² when x = 12 and y = 3.
31. 31.If a + b = 18 and ab = 77, what is a² + b²?
32. 32.If a + b = 11 and ab = 24, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 91².
34. 34.If a + b = 5 and ab = 6, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 97 × 83.
36. 36.Use (a + b)(a − b) = a² − b² to find 69 × 51.
37. 37.Use (a − b)² = a² − 2ab + b² to find 14².
38. 38.Use a² − b² = (a + b)(a − b) to find 40² − 5².
39. 39.Use (a − b)² = a² − 2ab + b² to find 67².
40. 40.Use (a + b)(a − b) = a² − b² to find 81 × 79.

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