Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 695 · 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 = 8 and y = 7.
2. 2.Use (a − b)² = a² − 2ab + b² to find 24².
3. 3.Use (a − b)² = a² − 2ab + b² to find 61².
4. 4.Use (a + b)(a − b) = a² − b² to find 22 × 18.
5. 5.Find the value of x² + 2xy + y² when x = 13 and y = 7.
6. 6.Use a² − b² = (a + b)(a − b) to find 29² − 3².
7. 7.Use (a + b)(a − b) = a² − b² to find 39 × 21.
8. 8.Use (a + b)² = a² + 2ab + b² to find 74².
9. 9.Use a² − b² = (a + b)(a − b) to find 95² − 8².
10. 10.Use a² − b² = (a + b)(a − b) to find 63² − 15².
11. 11.Use a² − b² = (a + b)(a − b) to find 45² − 37².
12. 12.Use (a + b)² = a² + 2ab + b² to find 94².
13. 13.If a + b = 12 and ab = 27, what is a² + b²?
14. 14.Find the value of x² + 2xy + y² when x = 13 and y = 9.
15. 15.Use a² − b² = (a + b)(a − b) to find 64² − 27².
16. 16.Use (a + b)² = a² + 2ab + b² to find 33².
17. 17.Use a² − b² = (a + b)(a − b) to find 58² − 11².
18. 18.If a + b = 10 and ab = 9, what is a² + b²?
19. 19.Find the value of x² − 2xy + y² when x = 12 and y = 4.
20. 20.If a + b = 11 and ab = 28, what is a² + b²?
21. 21.Find the value of x² − 2xy + y² when x = 4 and y = 1.
22. 22.Use (a − b)² = a² − 2ab + b² to find 28².
23. 23.If a − b = 5 and ab = 24, what is a² + b²?
24. 24.Find the value of x² − 2xy + y² when x = 5 and y = 2.
25. 25.Find the value of x² − 2xy + y² when x = 11 and y = 3.
26. 26.Use a² − b² = (a + b)(a − b) to find 72² − 70².
27. 27.If a + b = 18 and ab = 77, what is a² + b²?
28. 28.Find the value of x² − y² when x = 6 and y = 5.
29. 29.Use (a − b)² = a² − 2ab + b² to find 67².
30. 30.Use (a + b)² = a² + 2ab + b² to find 29².
31. 31.If a − b = 6 and ab = 40, what is a² + b²?
32. 32.Find the value of x² − y² when x = 5 and y = 2.
33. 33.Use a² − b² = (a + b)(a − b) to find 31² − 26².
34. 34.Use (a + b)² = a² + 2ab + b² to find 51².
35. 35.If a − b = 3 and ab = 4, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 72 × 68.
37. 37.Use (a + b)(a − b) = a² − b² to find 24 × 16.
38. 38.Find the value of x² + 2xy + y² when x = 12 and y = 1.
39. 39.Use (a + b)² = a² + 2ab + b² to find 25².
40. 40.If a + b = 8 and ab = 15, what is a² + b²?

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