Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 394 · 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 87² − 62².
2. 2.If a + b = 10 and ab = 24, what is a² + b²?
3. 3.If a + b = 12 and ab = 27, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 106².
5. 5.Use (a + b)² = a² + 2ab + b² to find 89².
6. 6.Use (a − b)² = a² − 2ab + b² to find 38².
7. 7.Use (a + b)(a − b) = a² − b² to find 75 × 65.
8. 8.Use (a + b)(a − b) = a² − b² to find 56 × 44.
9. 9.Find the value of x² − y² when x = 15 and y = 10.
10. 10.Use (a − b)² = a² − 2ab + b² to find 64².
11. 11.If a + b = 8 and ab = 15, what is a² + b²?
12. 12.Use (a + b)(a − b) = a² − b² to find 62 × 58.
13. 13.Use (a + b)² = a² + 2ab + b² to find 88².
14. 14.If a + b = 3 and ab = 2, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 11².
16. 16.Use (a + b)(a − b) = a² − b² to find 31 × 29.
17. 17.Use (a + b)² = a² + 2ab + b² to find 62².
18. 18.Use a² − b² = (a + b)(a − b) to find 93² − 2².
19. 19.If a − b = 9 and ab = 36, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 47².
21. 21.Find the value of x² − 2xy + y² when x = 8 and y = 6.
22. 22.Use (a + b)² = a² + 2ab + b² to find 103².
23. 23.Use (a + b)(a − b) = a² − b² to find 67 × 53.
24. 24.Use (a + b)² = a² + 2ab + b² to find 99².
25. 25.Use (a − b)² = a² − 2ab + b² to find 12².
26. 26.If a + b = 18 and ab = 80, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 57².
28. 28.If a − b = 2 and ab = 48, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 39² − 28².
30. 30.Use (a + b)(a − b) = a² − b² to find 78 × 62.
31. 31.Use (a + b)² = a² + 2ab + b² to find 16².
32. 32.Use (a + b)(a − b) = a² − b² to find 53 × 47.
33. 33.Use (a + b)(a − b) = a² − b² to find 33 × 27.
34. 34.Use a² − b² = (a + b)(a − b) to find 43² − 13².
35. 35.Use (a − b)² = a² − 2ab + b² to find 15².
36. 36.Find the value of x² + 2xy + y² when x = 5 and y = 1.
37. 37.If a − b = 2 and ab = 99, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 21².
39. 39.Find the value of x² − 2xy + y² when x = 14 and y = 1.
40. 40.Use (a − b)² = a² − 2ab + b² to find 42².

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