Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 459 · 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 = 2.
2. 2.Use (a + b)(a − b) = a² − b² to find 62 × 58.
3. 3.If a + b = 7 and ab = 12, what is a² + b²?
4. 4.Use (a + b)(a − b) = a² − b² to find 64 × 56.
5. 5.If a + b = 12 and ab = 27, what is a² + b²?
6. 6.If a − b = 3 and ab = 10, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 63² − 57².
8. 8.Use (a + b)² = a² + 2ab + b² to find 52².
9. 9.Use (a + b)² = a² + 2ab + b² to find 76².
10. 10.Use (a − b)² = a² − 2ab + b² to find 72².
11. 11.If a − b = 6 and ab = 7, what is a² + b²?
12. 12.Use (a + b)² = a² + 2ab + b² to find 97².
13. 13.Use (a − b)² = a² − 2ab + b² to find 29².
14. 14.Use (a + b)² = a² + 2ab + b² to find 56².
15. 15.Use (a − b)² = a² − 2ab + b² to find 53².
16. 16.Find the value of x² − 2xy + y² when x = 12 and y = 7.
17. 17.Use (a − b)² = a² − 2ab + b² to find 58².
18. 18.If a − b = 9 and ab = 22, what is a² + b²?
19. 19.Find the value of x² − y² when x = 12 and y = 10.
20. 20.Use a² − b² = (a + b)(a − b) to find 25² − 19².
21. 21.Use (a − b)² = a² − 2ab + b² to find 85².
22. 22.Use (a + b)² = a² + 2ab + b² to find 85².
23. 23.Use (a + b)² = a² + 2ab + b² to find 12².
24. 24.Use (a − b)² = a² − 2ab + b² to find 37².
25. 25.Use a² − b² = (a + b)(a − b) to find 20² − 1².
26. 26.Use (a − b)² = a² − 2ab + b² to find 28².
27. 27.Use (a − b)² = a² − 2ab + b² to find 69².
28. 28.Use (a + b)(a − b) = a² − b² to find 108 × 92.
29. 29.Use (a + b)(a − b) = a² − b² to find 22 × 18.
30. 30.Use (a + b)(a − b) = a² − b² to find 73 × 67.
31. 31.Find the value of x² + 2xy + y² when x = 10 and y = 3.
32. 32.Use (a − b)² = a² − 2ab + b² to find 34².
33. 33.Use (a − b)² = a² − 2ab + b² to find 76².
34. 34.Find the value of x² − y² when x = 13 and y = 3.
35. 35.Use (a − b)² = a² − 2ab + b² to find 17².
36. 36.Use (a + b)² = a² + 2ab + b² to find 89².
37. 37.Use (a + b)(a − b) = a² − b² to find 96 × 84.
38. 38.Use (a + b)(a − b) = a² − b² to find 104 × 96.
39. 39.Use a² − b² = (a + b)(a − b) to find 64² − 48².
40. 40.Find the value of x² − 2xy + y² when x = 9 and y = 4.

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