Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 872 · 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)(a − b) = a² − b² to find 23 × 17.
2. 2.Use (a + b)² = a² + 2ab + b² to find 41².
3. 3.Use a² − b² = (a + b)(a − b) to find 33² − 17².
4. 4.Use a² − b² = (a + b)(a − b) to find 21² − 8².
5. 5.Use (a + b)² = a² + 2ab + b² to find 62².
6. 6.If a − b = 1 and ab = 30, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 72² − 59².
8. 8.Use (a − b)² = a² − 2ab + b² to find 37².
9. 9.If a + b = 10 and ab = 21, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 94².
11. 11.If a + b = 4 and ab = 3, what is a² + b²?
12. 12.Find the value of x² + 2xy + y² when x = 3 and y = 2.
13. 13.Use (a + b)(a − b) = a² − b² to find 31 × 29.
14. 14.Use (a + b)² = a² + 2ab + b² to find 44².
15. 15.Use (a − b)² = a² − 2ab + b² to find 35².
16. 16.Find the value of x² + 2xy + y² when x = 10 and y = 5.
17. 17.If a + b = 5 and ab = 6, what is a² + b²?
18. 18.If a + b = 22 and ab = 120, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 42².
20. 20.Use (a + b)² = a² + 2ab + b² to find 43².
21. 21.Use (a + b)² = a² + 2ab + b² to find 32².
22. 22.Use (a + b)² = a² + 2ab + b² to find 47².
23. 23.Use a² − b² = (a + b)(a − b) to find 75² − 11².
24. 24.Use (a − b)² = a² − 2ab + b² to find 78².
25. 25.Find the value of x² − y² when x = 15 and y = 9.
26. 26.Use a² − b² = (a + b)(a − b) to find 67² − 48².
27. 27.Use (a − b)² = a² − 2ab + b² to find 13².
28. 28.Use (a + b)(a − b) = a² − b² to find 105 × 95.
29. 29.If a + b = 3 and ab = 2, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 59².
31. 31.Use a² − b² = (a + b)(a − b) to find 63² − 52².
32. 32.If a + b = 8 and ab = 15, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 22².
34. 34.Use (a − b)² = a² − 2ab + b² to find 55².
35. 35.Use (a − b)² = a² − 2ab + b² to find 52².
36. 36.Use (a + b)² = a² + 2ab + b² to find 13².
37. 37.If a + b = 14 and ab = 24, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 92².
39. 39.Use (a + b)² = a² + 2ab + b² to find 87².
40. 40.Use (a + b)(a − b) = a² − b² to find 52 × 48.

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