Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 485 · 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 = 6 and ab = 8, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 101².
3. 3.Use (a + b)² = a² + 2ab + b² to find 71².
4. 4.Use a² − b² = (a + b)(a − b) to find 72² − 21².
5. 5.Use (a + b)(a − b) = a² − b² to find 76 × 64.
6. 6.Use (a + b)² = a² + 2ab + b² to find 48².
7. 7.Use (a + b)(a − b) = a² − b² to find 51 × 49.
8. 8.Use (a + b)(a − b) = a² − b² to find 33 × 27.
9. 9.If a − b = 3 and ab = 28, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 35².
11. 11.Use (a + b)(a − b) = a² − b² to find 75 × 65.
12. 12.Use a² − b² = (a + b)(a − b) to find 90² − 5².
13. 13.Use a² − b² = (a + b)(a − b) to find 83² − 13².
14. 14.Use (a + b)(a − b) = a² − b² to find 82 × 78.
15. 15.Use (a + b)² = a² + 2ab + b² to find 24².
16. 16.Use (a + b)(a − b) = a² − b² to find 91 × 89.
17. 17.Use (a + b)(a − b) = a² − b² to find 92 × 88.
18. 18.If a − b = 1 and ab = 2, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 92².
20. 20.Find the value of x² − 2xy + y² when x = 15 and y = 13.
21. 21.Use (a + b)² = a² + 2ab + b² to find 29².
22. 22.Find the value of x² − 2xy + y² when x = 3 and y = 1.
23. 23.Use a² − b² = (a + b)(a − b) to find 69² − 38².
24. 24.If a − b = 3 and ab = 88, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 69².
26. 26.Find the value of x² − 2xy + y² when x = 9 and y = 1.
27. 27.Use (a + b)² = a² + 2ab + b² to find 62².
28. 28.Find the value of x² − 2xy + y² when x = 13 and y = 12.
29. 29.If a − b = 1 and ab = 6, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 25² − 16².
31. 31.Use (a − b)² = a² − 2ab + b² to find 41².
32. 32.Use (a + b)(a − b) = a² − b² to find 73 × 67.
33. 33.Use (a − b)² = a² − 2ab + b² to find 78².
34. 34.Use a² − b² = (a + b)(a − b) to find 98² − 76².
35. 35.Find the value of x² + 2xy + y² when x = 4 and y = 2.
36. 36.Find the value of x² − y² when x = 13 and y = 5.
37. 37.If a + b = 13 and ab = 30, what is a² + b²?
38. 38.Find the value of x² − 2xy + y² when x = 6 and y = 4.
39. 39.Use (a + b)² = a² + 2ab + b² to find 23².
40. 40.Use (a + b)² = a² + 2ab + b² to find 13².

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