Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 928 · 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 (a + b)² = a² + 2ab + b² to find 104².
2. 2.Use (a − b)² = a² − 2ab + b² to find 69².
3. 3.Use (a + b)(a − b) = a² − b² to find 68 × 52.
4. 4.Use a² − b² = (a + b)(a − b) to find 62² − 14².
5. 5.Use a² − b² = (a + b)(a − b) to find 68² − 11².
6. 6.Use (a + b)² = a² + 2ab + b² to find 88².
7. 7.If a − b = 2 and ab = 120, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 62 × 58.
9. 9.Use (a + b)(a − b) = a² − b² to find 34 × 26.
10. 10.If a − b = 2 and ab = 15, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 66 × 54.
12. 12.Find the value of x² − 2xy + y² when x = 5 and y = 1.
13. 13.Use (a + b)² = a² + 2ab + b² to find 107².
14. 14.If a + b = 11 and ab = 18, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 53² − 9².
16. 16.Use (a + b)(a − b) = a² − b² to find 96 × 84.
17. 17.If a + b = 7 and ab = 6, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 35 × 25.
19. 19.Use a² − b² = (a + b)(a − b) to find 93² − 17².
20. 20.Find the value of x² − 2xy + y² when x = 10 and y = 6.
21. 21.Use (a − b)² = a² − 2ab + b² to find 94².
22. 22.Find the value of x² − 2xy + y² when x = 7 and y = 6.
23. 23.Use (a − b)² = a² − 2ab + b² to find 78².
24. 24.Use a² − b² = (a + b)(a − b) to find 37² − 18².
25. 25.Find the value of x² − y² when x = 5 and y = 1.
26. 26.Use (a − b)² = a² − 2ab + b² to find 59².
27. 27.Use (a + b)² = a² + 2ab + b² to find 24².
28. 28.Find the value of x² − y² when x = 4 and y = 2.
29. 29.Use (a + b)² = a² + 2ab + b² to find 14².
30. 30.Use (a + b)² = a² + 2ab + b² to find 81².
31. 31.Use (a + b)(a − b) = a² − b² to find 98 × 82.
32. 32.Use (a + b)² = a² + 2ab + b² to find 17².
33. 33.Find the value of x² + 2xy + y² when x = 11 and y = 9.
34. 34.Use (a − b)² = a² − 2ab + b² to find 93².
35. 35.If a + b = 19 and ab = 84, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 74².
37. 37.Use (a + b)(a − b) = a² − b² to find 64 × 56.
38. 38.Use (a − b)² = a² − 2ab + b² to find 66².
39. 39.Use (a + b)² = a² + 2ab + b² to find 25².
40. 40.Use a² − b² = (a + b)(a − b) to find 74² − 2².

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