Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 836 · 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 − y² when x = 6 and y = 4.
2. 2.Use (a + b)² = a² + 2ab + b² to find 57².
3. 3.Use a² − b² = (a + b)(a − b) to find 81² − 48².
4. 4.If a − b = 7 and ab = 8, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 16².
6. 6.Use a² − b² = (a + b)(a − b) to find 98² − 49².
7. 7.If a − b = 2 and ab = 3, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 25².
9. 9.Use a² − b² = (a + b)(a − b) to find 98² − 47².
10. 10.Use a² − b² = (a + b)(a − b) to find 81² − 12².
11. 11.If a − b = 3 and ab = 70, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 40² − 23².
13. 13.Use (a − b)² = a² − 2ab + b² to find 72².
14. 14.Use (a + b)(a − b) = a² − b² to find 94 × 86.
15. 15.If a + b = 12 and ab = 11, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 71² − 27².
17. 17.If a − b = 5 and ab = 6, what is a² + b²?
18. 18.Use (a + b)² = a² + 2ab + b² to find 33².
19. 19.Use (a − b)² = a² − 2ab + b² to find 92².
20. 20.Use (a + b)² = a² + 2ab + b² to find 52².
21. 21.Use (a + b)(a − b) = a² − b² to find 88 × 72.
22. 22.If a + b = 17 and ab = 72, what is a² + b²?
23. 23.Use (a + b)² = a² + 2ab + b² to find 75².
24. 24.Use (a − b)² = a² − 2ab + b² to find 88².
25. 25.Find the value of x² − y² when x = 12 and y = 11.
26. 26.Use (a + b)(a − b) = a² − b² to find 51 × 49.
27. 27.Use (a + b)(a − b) = a² − b² to find 101 × 99.
28. 28.Use (a + b)² = a² + 2ab + b² to find 106².
29. 29.Use (a + b)(a − b) = a² − b² to find 86 × 74.
30. 30.Find the value of x² + 2xy + y² when x = 13 and y = 5.
31. 31.Use (a − b)² = a² − 2ab + b² to find 49².
32. 32.Use (a − b)² = a² − 2ab + b² to find 57².
33. 33.If a + b = 3 and ab = 2, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 72².
35. 35.Use (a − b)² = a² − 2ab + b² to find 96².
36. 36.Find the value of x² − 2xy + y² when x = 6 and y = 4.
37. 37.Use (a + b)(a − b) = a² − b² to find 91 × 89.
38. 38.Use (a + b)(a − b) = a² − b² to find 32 × 28.
39. 39.Use (a + b)² = a² + 2ab + b² to find 42².
40. 40.Use a² − b² = (a + b)(a − b) to find 45² − 4².

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