Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 678 · 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.If a + b = 10 and ab = 9, what is a² + b²?
2. 2.If a − b = 8 and ab = 20, what is a² + b²?
3. 3.If a − b = 4 and ab = 12, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 16².
5. 5.Use a² − b² = (a + b)(a − b) to find 52² − 33².
6. 6.Use (a − b)² = a² − 2ab + b² to find 14².
7. 7.Use a² − b² = (a + b)(a − b) to find 59² − 54².
8. 8.If a + b = 7 and ab = 10, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 24².
10. 10.Find the value of x² − y² when x = 6 and y = 5.
11. 11.Use (a + b)(a − b) = a² − b² to find 106 × 94.
12. 12.If a + b = 18 and ab = 80, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 66².
14. 14.Use (a + b)(a − b) = a² − b² to find 105 × 95.
15. 15.If a + b = 10 and ab = 21, what is a² + b²?
16. 16.Find the value of x² + 2xy + y² when x = 11 and y = 9.
17. 17.Find the value of x² − 2xy + y² when x = 7 and y = 1.
18. 18.Use (a + b)(a − b) = a² − b² to find 53 × 47.
19. 19.If a − b = 4 and ab = 21, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 13².
21. 21.Use (a − b)² = a² − 2ab + b² to find 24².
22. 22.Use (a + b)(a − b) = a² − b² to find 67 × 53.
23. 23.Use (a + b)(a − b) = a² − b² to find 43 × 37.
24. 24.Use (a + b)(a − b) = a² − b² to find 91 × 89.
25. 25.Use (a + b)² = a² + 2ab + b² to find 85².
26. 26.Use (a + b)(a − b) = a² − b² to find 24 × 16.
27. 27.Use (a − b)² = a² − 2ab + b² to find 46².
28. 28.If a + b = 6 and ab = 5, what is a² + b²?
29. 29.If a + b = 12 and ab = 32, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 89² − 68².
31. 31.Use (a − b)² = a² − 2ab + b² to find 17².
32. 32.Use (a − b)² = a² − 2ab + b² to find 25².
33. 33.Use (a + b)² = a² + 2ab + b² to find 39².
34. 34.Use (a − b)² = a² − 2ab + b² to find 93².
35. 35.Use a² − b² = (a + b)(a − b) to find 96² − 14².
36. 36.Use (a − b)² = a² − 2ab + b² to find 65².
37. 37.Use (a + b)² = a² + 2ab + b² to find 88².
38. 38.If a + b = 4 and ab = 3, what is a² + b²?
39. 39.Use (a + b)(a − b) = a² − b² to find 27 × 13.
40. 40.If a − b = 4 and ab = 45, what is a² + b²?

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