Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 962 · 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 89².
2. 2.Find the value of x² − y² when x = 8 and y = 5.
3. 3.Find the value of x² − 2xy + y² when x = 8 and y = 6.
4. 4.Use (a + b)² = a² + 2ab + b² to find 51².
5. 5.Use a² − b² = (a + b)(a − b) to find 24² − 12².
6. 6.Use (a + b)(a − b) = a² − b² to find 93 × 87.
7. 7.Use (a − b)² = a² − 2ab + b² to find 25².
8. 8.Use (a + b)² = a² + 2ab + b² to find 89².
9. 9.Use (a + b)² = a² + 2ab + b² to find 107².
10. 10.Use a² − b² = (a + b)(a − b) to find 62² − 6².
11. 11.Find the value of x² − y² when x = 15 and y = 12.
12. 12.Use (a + b)(a − b) = a² − b² to find 48 × 32.
13. 13.Find the value of x² + 2xy + y² when x = 9 and y = 1.
14. 14.Find the value of x² − 2xy + y² when x = 10 and y = 2.
15. 15.If a + b = 11 and ab = 10, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 80² − 51².
17. 17.Use a² − b² = (a + b)(a − b) to find 68² − 20².
18. 18.Use (a − b)² = a² − 2ab + b² to find 11².
19. 19.Use (a + b)² = a² + 2ab + b² to find 11².
20. 20.If a + b = 13 and ab = 40, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 71² − 3².
22. 22.Use (a − b)² = a² − 2ab + b² to find 26².
23. 23.If a + b = 16 and ab = 48, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 68 × 52.
25. 25.Find the value of x² − 2xy + y² when x = 15 and y = 14.
26. 26.Use (a + b)² = a² + 2ab + b² to find 94².
27. 27.Find the value of x² − 2xy + y² when x = 13 and y = 5.
28. 28.Find the value of x² − y² when x = 5 and y = 4.
29. 29.Use a² − b² = (a + b)(a − b) to find 57² − 38².
30. 30.Find the value of x² + 2xy + y² when x = 7 and y = 6.
31. 31.Find the value of x² + 2xy + y² when x = 13 and y = 3.
32. 32.Use (a − b)² = a² − 2ab + b² to find 14².
33. 33.Use (a − b)² = a² − 2ab + b² to find 52².
34. 34.Use (a − b)² = a² − 2ab + b² to find 88².
35. 35.Use (a + b)(a − b) = a² − b² to find 31 × 29.
36. 36.Use (a + b)(a − b) = a² − b² to find 26 × 14.
37. 37.Use (a + b)² = a² + 2ab + b² to find 65².
38. 38.Use (a + b)(a − b) = a² − b² to find 21 × 19.
39. 39.Use (a + b)(a − b) = a² − b² to find 102 × 98.
40. 40.Find the value of x² − y² when x = 5 and y = 2.

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