Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 156 · 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 87².
2. 2.Use (a − b)² = a² − 2ab + b² to find 17².
3. 3.Use (a + b)² = a² + 2ab + b² to find 104².
4. 4.Use a² − b² = (a + b)(a − b) to find 57² − 28².
5. 5.Use a² − b² = (a + b)(a − b) to find 45² − 25².
6. 6.Find the value of x² − 2xy + y² when x = 4 and y = 2.
7. 7.If a + b = 3 and ab = 2, what is a² + b²?
8. 8.Find the value of x² − 2xy + y² when x = 15 and y = 1.
9. 9.Find the value of x² + 2xy + y² when x = 14 and y = 10.
10. 10.Use (a − b)² = a² − 2ab + b² to find 23².
11. 11.Use (a + b)(a − b) = a² − b² to find 31 × 29.
12. 12.Use (a + b)² = a² + 2ab + b² to find 14².
13. 13.Use a² − b² = (a + b)(a − b) to find 30² − 14².
14. 14.Use (a + b)(a − b) = a² − b² to find 21 × 19.
15. 15.Use a² − b² = (a + b)(a − b) to find 63² − 60².
16. 16.Use (a − b)² = a² − 2ab + b² to find 99².
17. 17.Use a² − b² = (a + b)(a − b) to find 78² − 22².
18. 18.Use (a + b)² = a² + 2ab + b² to find 74².
19. 19.Use (a − b)² = a² − 2ab + b² to find 63².
20. 20.Find the value of x² − 2xy + y² when x = 15 and y = 13.
21. 21.Find the value of x² − y² when x = 7 and y = 2.
22. 22.Use a² − b² = (a + b)(a − b) to find 50² − 9².
23. 23.Use (a − b)² = a² − 2ab + b² to find 58².
24. 24.Use (a − b)² = a² − 2ab + b² to find 54².
25. 25.Use (a + b)² = a² + 2ab + b² to find 89².
26. 26.Use (a + b)² = a² + 2ab + b² to find 39².
27. 27.Use (a + b)² = a² + 2ab + b² to find 17².
28. 28.Use a² − b² = (a + b)(a − b) to find 43² − 5².
29. 29.If a + b = 4 and ab = 3, what is a² + b²?
30. 30.Find the value of x² + 2xy + y² when x = 9 and y = 6.
31. 31.Use (a + b)(a − b) = a² − b² to find 42 × 38.
32. 32.Find the value of x² − y² when x = 12 and y = 8.
33. 33.Use a² − b² = (a + b)(a − b) to find 67² − 33².
34. 34.Use (a + b)² = a² + 2ab + b² to find 25².
35. 35.Use (a − b)² = a² − 2ab + b² to find 36².
36. 36.Find the value of x² + 2xy + y² when x = 3 and y = 1.
37. 37.Find the value of x² − 2xy + y² when x = 10 and y = 6.
38. 38.Use (a − b)² = a² − 2ab + b² to find 92².
39. 39.Use (a − b)² = a² − 2ab + b² to find 29².
40. 40.Use (a + b)² = a² + 2ab + b² to find 16².

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