Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 19 · 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 = 9 and ab = 18, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 33².
3. 3.Use a² − b² = (a + b)(a − b) to find 27² − 3².
4. 4.Use (a − b)² = a² − 2ab + b² to find 33².
5. 5.Use (a + b)(a − b) = a² − b² to find 91 × 89.
6. 6.Use (a + b)² = a² + 2ab + b² to find 96².
7. 7.Find the value of x² − y² when x = 3 and y = 2.
8. 8.Use a² − b² = (a + b)(a − b) to find 31² − 12².
9. 9.Use (a − b)² = a² − 2ab + b² to find 32².
10. 10.Use (a + b)(a − b) = a² − b² to find 29 × 11.
11. 11.Use (a + b)² = a² + 2ab + b² to find 21².
12. 12.Use (a − b)² = a² − 2ab + b² to find 15².
13. 13.Use a² − b² = (a + b)(a − b) to find 42² − 41².
14. 14.Use (a − b)² = a² − 2ab + b² to find 22².
15. 15.Use (a + b)(a − b) = a² − b² to find 42 × 38.
16. 16.If a − b = 2 and ab = 48, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 34².
18. 18.Use (a − b)² = a² − 2ab + b² to find 92².
19. 19.Use a² − b² = (a + b)(a − b) to find 59² − 51².
20. 20.Use (a + b)² = a² + 2ab + b² to find 11².
21. 21.Use a² − b² = (a + b)(a − b) to find 61² − 59².
22. 22.Use (a + b)(a − b) = a² − b² to find 35 × 25.
23. 23.Use (a + b)² = a² + 2ab + b² to find 84².
24. 24.Use a² − b² = (a + b)(a − b) to find 95² − 67².
25. 25.Use (a + b)² = a² + 2ab + b² to find 14².
26. 26.Use (a + b)(a − b) = a² − b² to find 109 × 91.
27. 27.Use (a + b)² = a² + 2ab + b² to find 68².
28. 28.If a + b = 5 and ab = 4, what is a² + b²?
29. 29.Find the value of x² + 2xy + y² when x = 13 and y = 9.
30. 30.Use (a + b)² = a² + 2ab + b² to find 78².
31. 31.Find the value of x² − y² when x = 12 and y = 8.
32. 32.If a − b = 2 and ab = 3, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 85².
34. 34.Find the value of x² − 2xy + y² when x = 13 and y = 6.
35. 35.Use (a − b)² = a² − 2ab + b² to find 13².
36. 36.Use (a − b)² = a² − 2ab + b² to find 98².
37. 37.Use (a − b)² = a² − 2ab + b² to find 17².
38. 38.Use a² − b² = (a + b)(a − b) to find 23² − 13².
39. 39.Use a² − b² = (a + b)(a − b) to find 59² − 15².
40. 40.Find the value of x² + 2xy + y² when x = 14 and y = 3.

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