Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 135 · 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 a² − b² = (a + b)(a − b) to find 96² − 70².
2. 2.Use a² − b² = (a + b)(a − b) to find 41² − 6².
3. 3.Find the value of x² − 2xy + y² when x = 12 and y = 11.
4. 4.Use (a + b)² = a² + 2ab + b² to find 69².
5. 5.Use (a − b)² = a² − 2ab + b² to find 24².
6. 6.If a − b = 4 and ab = 5, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 54² − 34².
8. 8.Use (a − b)² = a² − 2ab + b² to find 99².
9. 9.Use (a + b)² = a² + 2ab + b² to find 29².
10. 10.Use (a + b)(a − b) = a² − b² to find 31 × 29.
11. 11.Use (a + b)² = a² + 2ab + b² to find 87².
12. 12.Find the value of x² − y² when x = 5 and y = 1.
13. 13.Use (a − b)² = a² − 2ab + b² to find 36².
14. 14.Use (a + b)² = a² + 2ab + b² to find 86².
15. 15.Find the value of x² − y² when x = 10 and y = 3.
16. 16.Use (a + b)² = a² + 2ab + b² to find 84².
17. 17.Find the value of x² − 2xy + y² when x = 10 and y = 3.
18. 18.Use (a − b)² = a² − 2ab + b² to find 52².
19. 19.Use (a − b)² = a² − 2ab + b² to find 98².
20. 20.Use (a − b)² = a² − 2ab + b² to find 46².
21. 21.Use a² − b² = (a + b)(a − b) to find 57² − 16².
22. 22.Use (a + b)(a − b) = a² − b² to find 93 × 87.
23. 23.Use (a + b)(a − b) = a² − b² to find 23 × 17.
24. 24.Use (a + b)(a − b) = a² − b² to find 105 × 95.
25. 25.Use (a − b)² = a² − 2ab + b² to find 39².
26. 26.Find the value of x² − y² when x = 9 and y = 1.
27. 27.Use (a + b)(a − b) = a² − b² to find 72 × 68.
28. 28.Use a² − b² = (a + b)(a − b) to find 93² − 70².
29. 29.Use a² − b² = (a + b)(a − b) to find 57² − 40².
30. 30.Use (a + b)² = a² + 2ab + b² to find 44².
31. 31.Use (a + b)² = a² + 2ab + b² to find 12².
32. 32.Use a² − b² = (a + b)(a − b) to find 66² − 32².
33. 33.Use (a − b)² = a² − 2ab + b² to find 28².
34. 34.Use a² − b² = (a + b)(a − b) to find 70² − 58².
35. 35.Use (a + b)² = a² + 2ab + b² to find 39².
36. 36.Use a² − b² = (a + b)(a − b) to find 35² − 10².
37. 37.Use (a + b)(a − b) = a² − b² to find 76 × 64.
38. 38.Use a² − b² = (a + b)(a − b) to find 40² − 38².
39. 39.If a + b = 16 and ab = 63, what is a² + b²?
40. 40.If a + b = 8 and ab = 15, what is a² + b²?

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