Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 524 · 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 63².
2. 2.If a + b = 7 and ab = 6, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 16².
4. 4.Use (a − b)² = a² − 2ab + b² to find 97².
5. 5.Use (a + b)² = a² + 2ab + b² to find 25².
6. 6.Use a² − b² = (a + b)(a − b) to find 50² − 16².
7. 7.Find the value of x² + 2xy + y² when x = 8 and y = 2.
8. 8.Use (a − b)² = a² − 2ab + b² to find 96².
9. 9.Use (a + b)² = a² + 2ab + b² to find 91².
10. 10.Use (a + b)(a − b) = a² − b² to find 41 × 39.
11. 11.Use (a + b)² = a² + 2ab + b² to find 72².
12. 12.Use (a − b)² = a² − 2ab + b² to find 87².
13. 13.Use (a + b)(a − b) = a² − b² to find 95 × 85.
14. 14.Find the value of x² + 2xy + y² when x = 9 and y = 2.
15. 15.Find the value of x² + 2xy + y² when x = 11 and y = 2.
16. 16.Find the value of x² − 2xy + y² when x = 9 and y = 7.
17. 17.Use (a − b)² = a² − 2ab + b² to find 49².
18. 18.Find the value of x² − 2xy + y² when x = 12 and y = 10.
19. 19.Use (a − b)² = a² − 2ab + b² to find 29².
20. 20.Use a² − b² = (a + b)(a − b) to find 43² − 18².
21. 21.Find the value of x² + 2xy + y² when x = 15 and y = 3.
22. 22.Use (a + b)² = a² + 2ab + b² to find 39².
23. 23.Use a² − b² = (a + b)(a − b) to find 36² − 17².
24. 24.Use (a − b)² = a² − 2ab + b² to find 42².
25. 25.If a + b = 16 and ab = 63, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 43².
27. 27.Use (a + b)² = a² + 2ab + b² to find 24².
28. 28.If a + b = 15 and ab = 44, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 14².
30. 30.Use (a − b)² = a² − 2ab + b² to find 47².
31. 31.If a + b = 20 and ab = 99, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 54² − 38².
33. 33.Use (a + b)² = a² + 2ab + b² to find 82².
34. 34.Use (a + b)² = a² + 2ab + b² to find 86².
35. 35.Use a² − b² = (a + b)(a − b) to find 91² − 12².
36. 36.Use (a − b)² = a² − 2ab + b² to find 62².
37. 37.Use (a − b)² = a² − 2ab + b² to find 44².
38. 38.Use (a − b)² = a² − 2ab + b² to find 82².
39. 39.Use (a + b)(a − b) = a² − b² to find 92 × 88.
40. 40.Find the value of x² − y² when x = 10 and y = 9.

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