Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 171 · 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 = 7 and y = 1.
2. 2.If a + b = 4 and ab = 3, what is a² + b²?
3. 3.If a + b = 6 and ab = 8, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 59².
5. 5.Find the value of x² − y² when x = 8 and y = 7.
6. 6.Use (a − b)² = a² − 2ab + b² to find 92².
7. 7.Use (a − b)² = a² − 2ab + b² to find 58².
8. 8.Use (a − b)² = a² − 2ab + b² to find 46².
9. 9.Find the value of x² + 2xy + y² when x = 6 and y = 3.
10. 10.Use (a + b)² = a² + 2ab + b² to find 17².
11. 11.Use (a + b)(a − b) = a² − b² to find 65 × 55.
12. 12.Use a² − b² = (a + b)(a − b) to find 76² − 35².
13. 13.Use (a + b)² = a² + 2ab + b² to find 106².
14. 14.Use (a + b)(a − b) = a² − b² to find 45 × 35.
15. 15.Use (a − b)² = a² − 2ab + b² to find 79².
16. 16.Use (a + b)² = a² + 2ab + b² to find 41².
17. 17.Use a² − b² = (a + b)(a − b) to find 74² − 56².
18. 18.Use a² − b² = (a + b)(a − b) to find 36² − 5².
19. 19.Use (a − b)² = a² − 2ab + b² to find 73².
20. 20.Find the value of x² + 2xy + y² when x = 8 and y = 1.
21. 21.Use (a + b)² = a² + 2ab + b² to find 36².
22. 22.Use (a + b)(a − b) = a² − b² to find 58 × 42.
23. 23.Use (a + b)² = a² + 2ab + b² to find 89².
24. 24.Use (a + b)(a − b) = a² − b² to find 42 × 38.
25. 25.Use a² − b² = (a + b)(a − b) to find 31² − 11².
26. 26.Use (a − b)² = a² − 2ab + b² to find 42².
27. 27.If a + b = 3 and ab = 2, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 87².
29. 29.Use (a − b)² = a² − 2ab + b² to find 47².
30. 30.Use (a + b)² = a² + 2ab + b² to find 109².
31. 31.Use (a − b)² = a² − 2ab + b² to find 32².
32. 32.Use (a + b)(a − b) = a² − b² to find 72 × 68.
33. 33.Use (a + b)(a − b) = a² − b² to find 107 × 93.
34. 34.If a − b = 5 and ab = 36, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 69² − 60².
36. 36.Use a² − b² = (a + b)(a − b) to find 60² − 2².
37. 37.If a − b = 7 and ab = 60, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 83².
39. 39.Use (a + b)² = a² + 2ab + b² to find 103².
40. 40.Use (a − b)² = a² − 2ab + b² to find 69².

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