Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 337 · 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.Use (a − b)² = a² − 2ab + b² to find 47².
2. 2.Use (a + b)(a − b) = a² − b² to find 71 × 69.
3. 3.If a + b = 6 and ab = 5, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 85².
5. 5.If a + b = 3 and ab = 2, what is a² + b²?
6. 6.If a − b = 9 and ab = 10, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 52² − 16².
8. 8.Use (a + b)² = a² + 2ab + b² to find 25².
9. 9.If a − b = 7 and ab = 60, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 55².
11. 11.Use a² − b² = (a + b)(a − b) to find 46² − 39².
12. 12.Use (a + b)² = a² + 2ab + b² to find 37².
13. 13.If a − b = 1 and ab = 6, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 15².
15. 15.Use (a + b)² = a² + 2ab + b² to find 56².
16. 16.Use (a + b)² = a² + 2ab + b² to find 81².
17. 17.Find the value of x² + 2xy + y² when x = 15 and y = 7.
18. 18.Use (a + b)² = a² + 2ab + b² to find 12².
19. 19.Use (a + b)(a − b) = a² − b² to find 68 × 52.
20. 20.Use (a − b)² = a² − 2ab + b² to find 88².
21. 21.Use (a + b)² = a² + 2ab + b² to find 92².
22. 22.Use (a + b)(a − b) = a² − b² to find 94 × 86.
23. 23.Use (a − b)² = a² − 2ab + b² to find 74².
24. 24.Use (a + b)² = a² + 2ab + b² to find 108².
25. 25.Use (a + b)² = a² + 2ab + b² to find 91².
26. 26.If a − b = 2 and ab = 3, what is a² + b²?
27. 27.If a − b = 5 and ab = 50, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 89² − 85².
29. 29.Find the value of x² + 2xy + y² when x = 4 and y = 1.
30. 30.Use (a + b)(a − b) = a² − b² to find 48 × 32.
31. 31.Use a² − b² = (a + b)(a − b) to find 97² − 47².
32. 32.Use (a + b)² = a² + 2ab + b² to find 87².
33. 33.Use a² − b² = (a + b)(a − b) to find 82² − 57².
34. 34.If a + b = 21 and ab = 110, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 45².
36. 36.Use (a + b)(a − b) = a² − b² to find 83 × 77.
37. 37.If a + b = 11 and ab = 28, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 97².
39. 39.Find the value of x² + 2xy + y² when x = 4 and y = 2.
40. 40.If a − b = 5 and ab = 24, what is a² + b²?

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