Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 89 · 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 = 4 and ab = 3, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 36².
3. 3.Use (a + b)² = a² + 2ab + b² to find 105².
4. 4.Use a² − b² = (a + b)(a − b) to find 40² − 36².
5. 5.If a − b = 5 and ab = 6, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 47².
7. 7.Use (a + b)(a − b) = a² − b² to find 81 × 79.
8. 8.Use (a − b)² = a² − 2ab + b² to find 99².
9. 9.If a − b = 2 and ab = 3, what is a² + b²?
10. 10.If a + b = 18 and ab = 80, what is a² + b²?
11. 11.If a + b = 12 and ab = 20, what is a² + b²?
12. 12.Find the value of x² − 2xy + y² when x = 7 and y = 5.
13. 13.If a + b = 5 and ab = 4, what is a² + b²?
14. 14.Find the value of x² − y² when x = 7 and y = 3.
15. 15.Find the value of x² − 2xy + y² when x = 13 and y = 6.
16. 16.Use a² − b² = (a + b)(a − b) to find 77² − 34².
17. 17.Use (a − b)² = a² − 2ab + b² to find 66².
18. 18.Use a² − b² = (a + b)(a − b) to find 30² − 21².
19. 19.Use (a + b)² = a² + 2ab + b² to find 18².
20. 20.Use a² − b² = (a + b)(a − b) to find 67² − 24².
21. 21.Use (a + b)(a − b) = a² − b² to find 65 × 55.
22. 22.Use (a + b)² = a² + 2ab + b² to find 25².
23. 23.Find the value of x² − y² when x = 14 and y = 10.
24. 24.Use (a + b)(a − b) = a² − b² to find 46 × 34.
25. 25.Use (a + b)² = a² + 2ab + b² to find 15².
26. 26.Use (a + b)(a − b) = a² − b² to find 63 × 57.
27. 27.Find the value of x² + 2xy + y² when x = 8 and y = 6.
28. 28.Use (a − b)² = a² − 2ab + b² to find 97².
29. 29.Use (a − b)² = a² − 2ab + b² to find 17².
30. 30.Use (a + b)(a − b) = a² − b² to find 52 × 48.
31. 31.Use (a + b)² = a² + 2ab + b² to find 37².
32. 32.If a − b = 2 and ab = 24, what is a² + b²?
33. 33.Find the value of x² − 2xy + y² when x = 6 and y = 1.
34. 34.Use (a − b)² = a² − 2ab + b² to find 48².
35. 35.Find the value of x² + 2xy + y² when x = 5 and y = 2.
36. 36.If a − b = 2 and ab = 35, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 59 × 41.
38. 38.Use (a + b)² = a² + 2ab + b² to find 107².
39. 39.Use (a + b)² = a² + 2ab + b² to find 17².
40. 40.Use (a + b)² = a² + 2ab + b² to find 88².

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