Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 181 · 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)(a − b) = a² − b² to find 27 × 13.
2. 2.If a + b = 5 and ab = 4, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 37² − 18².
4. 4.Use (a + b)² = a² + 2ab + b² to find 33².
5. 5.Use (a − b)² = a² − 2ab + b² to find 77².
6. 6.Use a² − b² = (a + b)(a − b) to find 78² − 39².
7. 7.Use (a + b)² = a² + 2ab + b² to find 36².
8. 8.If a + b = 17 and ab = 60, what is a² + b²?
9. 9.Find the value of x² − 2xy + y² when x = 6 and y = 4.
10. 10.Use (a + b)² = a² + 2ab + b² to find 83².
11. 11.Use (a + b)(a − b) = a² − b² to find 55 × 45.
12. 12.Use (a + b)(a − b) = a² − b² to find 56 × 44.
13. 13.Use (a + b)² = a² + 2ab + b² to find 41².
14. 14.Find the value of x² − y² when x = 5 and y = 2.
15. 15.Find the value of x² − 2xy + y² when x = 5 and y = 3.
16. 16.If a + b = 8 and ab = 7, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 35².
18. 18.Use (a − b)² = a² − 2ab + b² to find 44².
19. 19.Use (a + b)² = a² + 2ab + b² to find 16².
20. 20.Use (a + b)(a − b) = a² − b² to find 25 × 15.
21. 21.Use (a − b)² = a² − 2ab + b² to find 53².
22. 22.Use (a + b)(a − b) = a² − b² to find 73 × 67.
23. 23.If a + b = 12 and ab = 27, what is a² + b²?
24. 24.Use a² − b² = (a + b)(a − b) to find 47² − 3².
25. 25.Use a² − b² = (a + b)(a − b) to find 90² − 38².
26. 26.Find the value of x² − 2xy + y² when x = 5 and y = 4.
27. 27.Use (a + b)(a − b) = a² − b² to find 97 × 83.
28. 28.Use (a − b)² = a² − 2ab + b² to find 25².
29. 29.If a − b = 9 and ab = 22, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 29².
31. 31.Find the value of x² − 2xy + y² when x = 4 and y = 1.
32. 32.Use (a − b)² = a² − 2ab + b² to find 62².
33. 33.Use (a + b)² = a² + 2ab + b² to find 52².
34. 34.Use (a + b)² = a² + 2ab + b² to find 57².
35. 35.Use (a − b)² = a² − 2ab + b² to find 71².
36. 36.Find the value of x² + 2xy + y² when x = 11 and y = 7.
37. 37.Use a² − b² = (a + b)(a − b) to find 47² − 11².
38. 38.Use (a + b)(a − b) = a² − b² to find 29 × 11.
39. 39.Use (a + b)(a − b) = a² − b² to find 45 × 35.
40. 40.Use (a + b)(a − b) = a² − b² to find 69 × 51.

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