Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 348 · 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 = 12 and y = 4.
2. 2.Find the value of x² − 2xy + y² when x = 3 and y = 1.
3. 3.Use (a − b)² = a² − 2ab + b² to find 15².
4. 4.Find the value of x² − 2xy + y² when x = 6 and y = 1.
5. 5.Use a² − b² = (a + b)(a − b) to find 37² − 3².
6. 6.Use (a − b)² = a² − 2ab + b² to find 65².
7. 7.Use (a + b)(a − b) = a² − b² to find 21 × 19.
8. 8.Use (a + b)(a − b) = a² − b² to find 91 × 89.
9. 9.Use (a − b)² = a² − 2ab + b² to find 89².
10. 10.Use (a − b)² = a² − 2ab + b² to find 64².
11. 11.Use (a + b)² = a² + 2ab + b² to find 79².
12. 12.Find the value of x² − y² when x = 4 and y = 1.
13. 13.Use (a + b)² = a² + 2ab + b² to find 64².
14. 14.Use (a + b)² = a² + 2ab + b² to find 73².
15. 15.Use (a − b)² = a² − 2ab + b² to find 69².
16. 16.Use a² − b² = (a + b)(a − b) to find 28² − 27².
17. 17.Use a² − b² = (a + b)(a − b) to find 27² − 16².
18. 18.Use (a − b)² = a² − 2ab + b² to find 21².
19. 19.Use (a + b)² = a² + 2ab + b² to find 62².
20. 20.Use (a + b)(a − b) = a² − b² to find 52 × 48.
21. 21.Use (a + b)(a − b) = a² − b² to find 58 × 42.
22. 22.Use a² − b² = (a + b)(a − b) to find 69² − 5².
23. 23.Use (a + b)(a − b) = a² − b² to find 33 × 27.
24. 24.If a + b = 5 and ab = 6, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 28 × 12.
26. 26.Find the value of x² + 2xy + y² when x = 7 and y = 2.
27. 27.Find the value of x² + 2xy + y² when x = 12 and y = 6.
28. 28.Use (a + b)(a − b) = a² − b² to find 104 × 96.
29. 29.Use (a + b)(a − b) = a² − b² to find 89 × 71.
30. 30.Use (a + b)² = a² + 2ab + b² to find 52².
31. 31.Use (a − b)² = a² − 2ab + b² to find 97².
32. 32.If a + b = 6 and ab = 8, what is a² + b²?
33. 33.Find the value of x² − 2xy + y² when x = 12 and y = 2.
34. 34.Use (a + b)(a − b) = a² − b² to find 108 × 92.
35. 35.Use (a − b)² = a² − 2ab + b² to find 57².
36. 36.If a + b = 8 and ab = 12, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 98² − 14².
38. 38.Use (a + b)(a − b) = a² − b² to find 37 × 23.
39. 39.If a + b = 7 and ab = 12, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 68 × 52.

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