Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 498 · 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 = 5 and y = 4.
2. 2.Use (a − b)² = a² − 2ab + b² to find 47².
3. 3.Use (a + b)² = a² + 2ab + b² to find 24².
4. 4.Use (a − b)² = a² − 2ab + b² to find 64².
5. 5.Find the value of x² + 2xy + y² when x = 15 and y = 14.
6. 6.Find the value of x² − y² when x = 7 and y = 4.
7. 7.Use (a + b)(a − b) = a² − b² to find 62 × 58.
8. 8.If a − b = 6 and ab = 16, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 81².
10. 10.If a − b = 2 and ab = 8, what is a² + b²?
11. 11.Find the value of x² + 2xy + y² when x = 4 and y = 2.
12. 12.Use a² − b² = (a + b)(a − b) to find 97² − 70².
13. 13.Use (a − b)² = a² − 2ab + b² to find 16².
14. 14.Use (a + b)(a − b) = a² − b² to find 74 × 66.
15. 15.Use (a + b)² = a² + 2ab + b² to find 45².
16. 16.Find the value of x² + 2xy + y² when x = 9 and y = 6.
17. 17.Use a² − b² = (a + b)(a − b) to find 42² − 31².
18. 18.Use (a − b)² = a² − 2ab + b² to find 88².
19. 19.Use a² − b² = (a + b)(a − b) to find 22² − 4².
20. 20.Use (a + b)(a − b) = a² − b² to find 77 × 63.
21. 21.Find the value of x² − 2xy + y² when x = 13 and y = 12.
22. 22.Use a² − b² = (a + b)(a − b) to find 95² − 60².
23. 23.Find the value of x² − y² when x = 12 and y = 10.
24. 24.Use (a + b)(a − b) = a² − b² to find 24 × 16.
25. 25.Use (a + b)(a − b) = a² − b² to find 48 × 32.
26. 26.If a − b = 3 and ab = 70, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 11².
28. 28.Use (a + b)² = a² + 2ab + b² to find 38².
29. 29.Use (a + b)(a − b) = a² − b² to find 76 × 64.
30. 30.Use (a + b)² = a² + 2ab + b² to find 93².
31. 31.Use a² − b² = (a + b)(a − b) to find 29² − 27².
32. 32.If a + b = 21 and ab = 108, what is a² + b²?
33. 33.Find the value of x² + 2xy + y² when x = 5 and y = 2.
34. 34.Find the value of x² + 2xy + y² when x = 13 and y = 4.
35. 35.Use (a − b)² = a² − 2ab + b² to find 61².
36. 36.Use (a + b)(a − b) = a² − b² to find 82 × 78.
37. 37.Use a² − b² = (a + b)(a − b) to find 43² − 33².
38. 38.Use (a − b)² = a² − 2ab + b² to find 46².
39. 39.Use a² − b² = (a + b)(a − b) to find 87² − 64².
40. 40.Use (a − b)² = a² − 2ab + b² to find 77².

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