Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 803 · 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.If a − b = 1 and ab = 110, what is a² + b²?
2. 2.Find the value of x² − 2xy + y² when x = 14 and y = 11.
3. 3.Use (a − b)² = a² − 2ab + b² to find 16².
4. 4.Use (a + b)² = a² + 2ab + b² to find 65².
5. 5.Find the value of x² − 2xy + y² when x = 13 and y = 3.
6. 6.Find the value of x² − y² when x = 4 and y = 3.
7. 7.Use (a − b)² = a² − 2ab + b² to find 45².
8. 8.Use (a + b)(a − b) = a² − b² to find 46 × 34.
9. 9.Use (a − b)² = a² − 2ab + b² to find 15².
10. 10.Use (a − b)² = a² − 2ab + b² to find 78².
11. 11.Use (a + b)² = a² + 2ab + b² to find 63².
12. 12.Find the value of x² − y² when x = 6 and y = 2.
13. 13.Find the value of x² − y² when x = 8 and y = 4.
14. 14.Use (a + b)(a − b) = a² − b² to find 51 × 49.
15. 15.Use (a + b)(a − b) = a² − b² to find 93 × 87.
16. 16.Find the value of x² + 2xy + y² when x = 14 and y = 13.
17. 17.Find the value of x² − 2xy + y² when x = 4 and y = 1.
18. 18.If a − b = 4 and ab = 32, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 87².
20. 20.Use a² − b² = (a + b)(a − b) to find 70² − 35².
21. 21.Use (a − b)² = a² − 2ab + b² to find 38².
22. 22.Use (a − b)² = a² − 2ab + b² to find 67².
23. 23.Use (a + b)(a − b) = a² − b² to find 88 × 72.
24. 24.Use a² − b² = (a + b)(a − b) to find 60² − 47².
25. 25.If a − b = 3 and ab = 18, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 26².
27. 27.Use (a + b)² = a² + 2ab + b² to find 93².
28. 28.Use (a − b)² = a² − 2ab + b² to find 83².
29. 29.Use (a − b)² = a² − 2ab + b² to find 17².
30. 30.Find the value of x² + 2xy + y² when x = 5 and y = 2.
31. 31.Find the value of x² − 2xy + y² when x = 5 and y = 3.
32. 32.Use (a − b)² = a² − 2ab + b² to find 23².
33. 33.Use (a − b)² = a² − 2ab + b² to find 13².
34. 34.Use (a + b)² = a² + 2ab + b² to find 69².
35. 35.Use a² − b² = (a + b)(a − b) to find 55² − 18².
36. 36.Use a² − b² = (a + b)(a − b) to find 70² − 12².
37. 37.If a + b = 11 and ab = 28, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 101 × 99.
39. 39.Use (a + b)(a − b) = a² − b² to find 62 × 58.
40. 40.Use (a − b)² = a² − 2ab + b² to find 42².

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