Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 336 · 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 = 9 and y = 2.
2. 2.Use (a + b)² = a² + 2ab + b² to find 31².
3. 3.Use (a − b)² = a² − 2ab + b² to find 96².
4. 4.Use (a − b)² = a² − 2ab + b² to find 57².
5. 5.Find the value of x² + 2xy + y² when x = 11 and y = 3.
6. 6.If a + b = 3 and ab = 2, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 37².
8. 8.If a − b = 2 and ab = 99, what is a² + b²?
9. 9.If a + b = 5 and ab = 4, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 62².
11. 11.Use (a − b)² = a² − 2ab + b² to find 29².
12. 12.Use (a + b)² = a² + 2ab + b² to find 12².
13. 13.Use (a + b)(a − b) = a² − b² to find 56 × 44.
14. 14.Use a² − b² = (a + b)(a − b) to find 97² − 63².
15. 15.Use (a + b)(a − b) = a² − b² to find 53 × 47.
16. 16.Use (a + b)(a − b) = a² − b² to find 52 × 48.
17. 17.Use a² − b² = (a + b)(a − b) to find 21² − 9².
18. 18.Use (a − b)² = a² − 2ab + b² to find 15².
19. 19.Use (a − b)² = a² − 2ab + b² to find 36².
20. 20.Find the value of x² + 2xy + y² when x = 4 and y = 1.
21. 21.Find the value of x² + 2xy + y² when x = 8 and y = 2.
22. 22.Find the value of x² + 2xy + y² when x = 11 and y = 5.
23. 23.Use (a + b)² = a² + 2ab + b² to find 63².
24. 24.If a + b = 5 and ab = 6, what is a² + b²?
25. 25.Find the value of x² − 2xy + y² when x = 5 and y = 4.
26. 26.Find the value of x² − 2xy + y² when x = 4 and y = 3.
27. 27.Use (a + b)(a − b) = a² − b² to find 31 × 29.
28. 28.Use a² − b² = (a + b)(a − b) to find 21² − 5².
29. 29.Find the value of x² + 2xy + y² when x = 4 and y = 2.
30. 30.Use (a + b)² = a² + 2ab + b² to find 92².
31. 31.Use a² − b² = (a + b)(a − b) to find 90² − 16².
32. 32.Use a² − b² = (a + b)(a − b) to find 23² − 11².
33. 33.Use (a − b)² = a² − 2ab + b² to find 87².
34. 34.Use a² − b² = (a + b)(a − b) to find 63² − 5².
35. 35.Use (a − b)² = a² − 2ab + b² to find 79².
36. 36.Use (a + b)² = a² + 2ab + b² to find 26².
37. 37.Find the value of x² + 2xy + y² when x = 10 and y = 7.
38. 38.Use a² − b² = (a + b)(a − b) to find 37² − 5².
39. 39.Use (a + b)(a − b) = a² − b² to find 72 × 68.
40. 40.Use (a − b)² = a² − 2ab + b² to find 31².

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