Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 292 · 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 99² − 67².
2. 2.Find the value of x² − 2xy + y² when x = 8 and y = 1.
3. 3.Find the value of x² − y² when x = 15 and y = 3.
4. 4.Use (a + b)² = a² + 2ab + b² to find 57².
5. 5.Use (a + b)² = a² + 2ab + b² to find 49².
6. 6.Use (a + b)² = a² + 2ab + b² to find 61².
7. 7.Use (a + b)² = a² + 2ab + b² to find 103².
8. 8.Use (a + b)² = a² + 2ab + b² to find 65².
9. 9.Use a² − b² = (a + b)(a − b) to find 95² − 13².
10. 10.Use (a − b)² = a² − 2ab + b² to find 38².
11. 11.Use (a − b)² = a² − 2ab + b² to find 16².
12. 12.Use a² − b² = (a + b)(a − b) to find 89² − 48².
13. 13.Use (a − b)² = a² − 2ab + b² to find 58².
14. 14.Find the value of x² − 2xy + y² when x = 11 and y = 1.
15. 15.If a + b = 6 and ab = 8, what is a² + b²?
16. 16.If a − b = 2 and ab = 3, what is a² + b²?
17. 17.Use (a + b)(a − b) = a² − b² to find 43 × 37.
18. 18.If a − b = 7 and ab = 8, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 17².
20. 20.Use (a + b)² = a² + 2ab + b² to find 82².
21. 21.Use (a + b)² = a² + 2ab + b² to find 98².
22. 22.Use a² − b² = (a + b)(a − b) to find 61² − 46².
23. 23.Use a² − b² = (a + b)(a − b) to find 83² − 79².
24. 24.Use (a + b)(a − b) = a² − b² to find 71 × 69.
25. 25.Find the value of x² − y² when x = 4 and y = 2.
26. 26.Use (a + b)² = a² + 2ab + b² to find 11².
27. 27.Use a² − b² = (a + b)(a − b) to find 66² − 33².
28. 28.Use (a − b)² = a² − 2ab + b² to find 75².
29. 29.Use (a + b)² = a² + 2ab + b² to find 23².
30. 30.Use (a + b)² = a² + 2ab + b² to find 79².
31. 31.Find the value of x² + 2xy + y² when x = 14 and y = 3.
32. 32.Use (a + b)(a − b) = a² − b² to find 25 × 15.
33. 33.Use (a + b)² = a² + 2ab + b² to find 34².
34. 34.Use (a − b)² = a² − 2ab + b² to find 24².
35. 35.Use a² − b² = (a + b)(a − b) to find 77² − 13².
36. 36.If a + b = 11 and ab = 18, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 32 × 28.
38. 38.Find the value of x² − 2xy + y² when x = 15 and y = 11.
39. 39.Use (a + b)² = a² + 2ab + b² to find 12².
40. 40.If a + b = 19 and ab = 90, what is a² + b²?

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