Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 816 · 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.If a + b = 14 and ab = 40, what is a² + b²?
2. 2.Find the value of x² − y² when x = 13 and y = 10.
3. 3.Use (a + b)(a − b) = a² − b² to find 89 × 71.
4. 4.Use a² − b² = (a + b)(a − b) to find 83² − 9².
5. 5.Use (a − b)² = a² − 2ab + b² to find 99².
6. 6.Use a² − b² = (a + b)(a − b) to find 42² − 10².
7. 7.Use (a + b)(a − b) = a² − b² to find 49 × 31.
8. 8.If a + b = 6 and ab = 8, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 11².
10. 10.Use a² − b² = (a + b)(a − b) to find 85² − 60².
11. 11.Find the value of x² − y² when x = 10 and y = 4.
12. 12.Use (a + b)(a − b) = a² − b² to find 21 × 19.
13. 13.Use (a − b)² = a² − 2ab + b² to find 86².
14. 14.Use a² − b² = (a + b)(a − b) to find 89² − 36².
15. 15.Use (a + b)² = a² + 2ab + b² to find 16².
16. 16.Use a² − b² = (a + b)(a − b) to find 80² − 39².
17. 17.Use (a + b)² = a² + 2ab + b² to find 91².
18. 18.If a + b = 5 and ab = 4, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 46².
20. 20.Use (a + b)² = a² + 2ab + b² to find 84².
21. 21.Use a² − b² = (a + b)(a − b) to find 35² − 4².
22. 22.Use (a − b)² = a² − 2ab + b² to find 12².
23. 23.Use (a + b)(a − b) = a² − b² to find 58 × 42.
24. 24.Use (a + b)² = a² + 2ab + b² to find 15².
25. 25.Find the value of x² + 2xy + y² when x = 14 and y = 11.
26. 26.Use a² − b² = (a + b)(a − b) to find 39² − 11².
27. 27.Use a² − b² = (a + b)(a − b) to find 49² − 36².
28. 28.Find the value of x² − 2xy + y² when x = 6 and y = 3.
29. 29.Use (a + b)² = a² + 2ab + b² to find 24².
30. 30.Use (a + b)(a − b) = a² − b² to find 35 × 25.
31. 31.Find the value of x² + 2xy + y² when x = 4 and y = 3.
32. 32.Use (a + b)² = a² + 2ab + b² to find 39².
33. 33.Use (a + b)(a − b) = a² − b² to find 45 × 35.
34. 34.Use (a + b)(a − b) = a² − b² to find 27 × 13.
35. 35.Use (a + b)² = a² + 2ab + b² to find 38².
36. 36.Use a² − b² = (a + b)(a − b) to find 23² − 4².
37. 37.Use (a + b)² = a² + 2ab + b² to find 82².
38. 38.If a + b = 11 and ab = 28, what is a² + b²?
39. 39.Use (a + b)(a − b) = a² − b² to find 71 × 69.
40. 40.Use (a + b)(a − b) = a² − b² to find 41 × 39.

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