Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 555 · 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 14².
2. 2.Use (a + b)(a − b) = a² − b² to find 45 × 35.
3. 3.Find the value of x² − y² when x = 6 and y = 5.
4. 4.If a + b = 11 and ab = 30, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 74².
6. 6.If a + b = 15 and ab = 50, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 94² − 58².
8. 8.Use (a − b)² = a² − 2ab + b² to find 54².
9. 9.Use (a + b)² = a² + 2ab + b² to find 13².
10. 10.Use a² − b² = (a + b)(a − b) to find 70² − 48².
11. 11.Use (a + b)(a − b) = a² − b² to find 51 × 49.
12. 12.Use a² − b² = (a + b)(a − b) to find 83² − 45².
13. 13.Use a² − b² = (a + b)(a − b) to find 82² − 47².
14. 14.If a + b = 3 and ab = 2, what is a² + b²?
15. 15.If a + b = 13 and ab = 12, what is a² + b²?
16. 16.If a − b = 2 and ab = 3, what is a² + b²?
17. 17.If a − b = 5 and ab = 14, what is a² + b²?
18. 18.If a − b = 2 and ab = 8, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 97².
20. 20.Use (a − b)² = a² − 2ab + b² to find 29².
21. 21.If a − b = 3 and ab = 4, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 89².
23. 23.Find the value of x² − y² when x = 11 and y = 2.
24. 24.Use (a + b)(a − b) = a² − b² to find 89 × 71.
25. 25.Use (a + b)² = a² + 2ab + b² to find 55².
26. 26.Use (a − b)² = a² − 2ab + b² to find 77².
27. 27.Use (a − b)² = a² − 2ab + b² to find 17².
28. 28.If a + b = 10 and ab = 21, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 81².
30. 30.Use (a + b)(a − b) = a² − b² to find 91 × 89.
31. 31.Use (a + b)(a − b) = a² − b² to find 35 × 25.
32. 32.Use (a − b)² = a² − 2ab + b² to find 75².
33. 33.Use (a − b)² = a² − 2ab + b² to find 85².
34. 34.Find the value of x² − 2xy + y² when x = 5 and y = 4.
35. 35.If a + b = 7 and ab = 6, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 22².
37. 37.Use a² − b² = (a + b)(a − b) to find 86² − 61².
38. 38.If a − b = 4 and ab = 5, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 60² − 34².
40. 40.Use (a + b)(a − b) = a² − b² to find 37 × 23.

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