Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 497 · 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.Find the value of x² + 2xy + y² when x = 3 and y = 2.
2. 2.Use a² − b² = (a + b)(a − b) to find 48² − 37².
3. 3.Use (a + b)(a − b) = a² − b² to find 84 × 76.
4. 4.Use (a + b)² = a² + 2ab + b² to find 61².
5. 5.Use (a − b)² = a² − 2ab + b² to find 35².
6. 6.Use (a + b)(a − b) = a² − b² to find 23 × 17.
7. 7.Find the value of x² − y² when x = 13 and y = 1.
8. 8.Use (a − b)² = a² − 2ab + b² to find 97².
9. 9.Use (a − b)² = a² − 2ab + b² to find 65².
10. 10.Use (a + b)² = a² + 2ab + b² to find 51².
11. 11.Use a² − b² = (a + b)(a − b) to find 53² − 12².
12. 12.Use (a + b)(a − b) = a² − b² to find 109 × 91.
13. 13.Use (a + b)(a − b) = a² − b² to find 98 × 82.
14. 14.Use (a + b)² = a² + 2ab + b² to find 29².
15. 15.Use (a + b)(a − b) = a² − b² to find 71 × 69.
16. 16.If a + b = 5 and ab = 4, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 82² − 17².
18. 18.Find the value of x² + 2xy + y² when x = 7 and y = 5.
19. 19.Use (a + b)(a − b) = a² − b² to find 97 × 83.
20. 20.Use (a + b)(a − b) = a² − b² to find 83 × 77.
21. 21.If a + b = 13 and ab = 12, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 49² − 45².
23. 23.If a − b = 1 and ab = 2, what is a² + b²?
24. 24.Use (a + b)² = a² + 2ab + b² to find 93².
25. 25.Use (a + b)² = a² + 2ab + b² to find 87².
26. 26.Use a² − b² = (a + b)(a − b) to find 36² − 8².
27. 27.Find the value of x² − 2xy + y² when x = 13 and y = 9.
28. 28.If a − b = 5 and ab = 66, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 53 × 47.
30. 30.Find the value of x² − 2xy + y² when x = 7 and y = 2.
31. 31.If a − b = 7 and ab = 30, what is a² + b²?
32. 32.Find the value of x² + 2xy + y² when x = 4 and y = 3.
33. 33.Use (a − b)² = a² − 2ab + b² to find 67².
34. 34.Find the value of x² − y² when x = 4 and y = 1.
35. 35.Find the value of x² − y² when x = 7 and y = 4.
36. 36.Use a² − b² = (a + b)(a − b) to find 73² − 48².
37. 37.Find the value of x² + 2xy + y² when x = 9 and y = 3.
38. 38.Find the value of x² + 2xy + y² when x = 15 and y = 5.
39. 39.Use (a − b)² = a² − 2ab + b² to find 38².
40. 40.If a − b = 2 and ab = 63, what is a² + b²?

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