Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 466 · 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.Find the value of x² − 2xy + y² when x = 5 and y = 2.
2. 2.Find the value of x² − 2xy + y² when x = 4 and y = 2.
3. 3.Use (a + b)² = a² + 2ab + b² to find 12².
4. 4.Use a² − b² = (a + b)(a − b) to find 23² − 7².
5. 5.If a + b = 12 and ab = 27, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 54 × 46.
7. 7.Use (a + b)² = a² + 2ab + b² to find 15².
8. 8.Use (a + b)² = a² + 2ab + b² to find 101².
9. 9.Use (a + b)(a − b) = a² − b² to find 44 × 36.
10. 10.Find the value of x² + 2xy + y² when x = 3 and y = 2.
11. 11.Use a² − b² = (a + b)(a − b) to find 59² − 41².
12. 12.Use (a + b)(a − b) = a² − b² to find 93 × 87.
13. 13.Use (a + b)(a − b) = a² − b² to find 61 × 59.
14. 14.Find the value of x² − y² when x = 12 and y = 2.
15. 15.If a − b = 1 and ab = 90, what is a² + b²?
16. 16.If a − b = 4 and ab = 60, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 74².
18. 18.Use (a + b)² = a² + 2ab + b² to find 92².
19. 19.Use a² − b² = (a + b)(a − b) to find 50² − 9².
20. 20.Use a² − b² = (a + b)(a − b) to find 85² − 6².
21. 21.Use a² − b² = (a + b)(a − b) to find 72² − 40².
22. 22.If a + b = 16 and ab = 55, what is a² + b²?
23. 23.If a − b = 2 and ab = 120, what is a² + b²?
24. 24.Find the value of x² − y² when x = 11 and y = 8.
25. 25.Use a² − b² = (a + b)(a − b) to find 99² − 70².
26. 26.Use (a + b)² = a² + 2ab + b² to find 11².
27. 27.Use (a + b)(a − b) = a² − b² to find 72 × 68.
28. 28.Use a² − b² = (a + b)(a − b) to find 75² − 65².
29. 29.Use (a + b)(a − b) = a² − b² to find 103 × 97.
30. 30.Use a² − b² = (a + b)(a − b) to find 36² − 19².
31. 31.If a − b = 3 and ab = 54, what is a² + b²?
32. 32.If a + b = 5 and ab = 6, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 51 × 49.
34. 34.Use (a + b)² = a² + 2ab + b² to find 71².
35. 35.Use a² − b² = (a + b)(a − b) to find 81² − 53².
36. 36.Use (a + b)(a − b) = a² − b² to find 36 × 24.
37. 37.Use (a − b)² = a² − 2ab + b² to find 21².
38. 38.Use (a − b)² = a² − 2ab + b² to find 13².
39. 39.Use (a − b)² = a² − 2ab + b² to find 98².
40. 40.Use (a − b)² = a² − 2ab + b² to find 23².

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