Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 577 · 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 a² − b² = (a + b)(a − b) to find 61² − 34².
2. 2.If a + b = 9 and ab = 8, what is a² + b²?
3. 3.Find the value of x² − y² when x = 7 and y = 3.
4. 4.Use a² − b² = (a + b)(a − b) to find 46² − 41².
5. 5.Use (a + b)² = a² + 2ab + b² to find 21².
6. 6.Use (a + b)² = a² + 2ab + b² to find 18².
7. 7.Use (a + b)² = a² + 2ab + b² to find 22².
8. 8.Use (a − b)² = a² − 2ab + b² to find 93².
9. 9.If a − b = 2 and ab = 8, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 25² − 21².
11. 11.Use a² − b² = (a + b)(a − b) to find 44² − 17².
12. 12.Use (a + b)² = a² + 2ab + b² to find 38².
13. 13.Use a² − b² = (a + b)(a − b) to find 48² − 42².
14. 14.Use (a − b)² = a² − 2ab + b² to find 34².
15. 15.Use (a + b)² = a² + 2ab + b² to find 13².
16. 16.Use (a + b)(a − b) = a² − b² to find 46 × 34.
17. 17.If a + b = 11 and ab = 28, what is a² + b²?
18. 18.If a − b = 7 and ab = 18, what is a² + b²?
19. 19.Find the value of x² − 2xy + y² when x = 11 and y = 8.
20. 20.Use (a + b)(a − b) = a² − b² to find 31 × 29.
21. 21.Use a² − b² = (a + b)(a − b) to find 63² − 14².
22. 22.Use a² − b² = (a + b)(a − b) to find 68² − 37².
23. 23.If a + b = 10 and ab = 16, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 88².
25. 25.Use (a + b)(a − b) = a² − b² to find 73 × 67.
26. 26.Use a² − b² = (a + b)(a − b) to find 53² − 31².
27. 27.Use a² − b² = (a + b)(a − b) to find 84² − 56².
28. 28.Use (a + b)² = a² + 2ab + b² to find 29².
29. 29.Use (a + b)(a − b) = a² − b² to find 89 × 71.
30. 30.Use (a + b)(a − b) = a² − b² to find 21 × 19.
31. 31.If a + b = 6 and ab = 5, what is a² + b²?
32. 32.If a + b = 6 and ab = 8, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 32².
34. 34.If a + b = 14 and ab = 24, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 97² − 1².
36. 36.Use (a + b)² = a² + 2ab + b² to find 101².
37. 37.If a + b = 8 and ab = 15, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 52 × 48.
39. 39.Use (a + b)² = a² + 2ab + b² to find 97².
40. 40.If a + b = 8 and ab = 12, what is a² + b²?

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