Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 845 · 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 = 2 and ab = 35, 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 79².
4. 4.Use (a + b)(a − b) = a² − b² to find 22 × 18.
5. 5.Use a² − b² = (a + b)(a − b) to find 99² − 2².
6. 6.Use (a − b)² = a² − 2ab + b² to find 73².
7. 7.Use (a − b)² = a² − 2ab + b² to find 59².
8. 8.Use a² − b² = (a + b)(a − b) to find 67² − 31².
9. 9.Use (a + b)(a − b) = a² − b² to find 91 × 89.
10. 10.Use (a − b)² = a² − 2ab + b² to find 46².
11. 11.If a + b = 13 and ab = 42, what is a² + b²?
12. 12.If a + b = 3 and ab = 2, what is a² + b²?
13. 13.If a − b = 2 and ab = 3, what is a² + b²?
14. 14.If a − b = 1 and ab = 30, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 18².
16. 16.Use a² − b² = (a + b)(a − b) to find 28² − 12².
17. 17.If a − b = 3 and ab = 4, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 41 × 39.
19. 19.Use (a − b)² = a² − 2ab + b² to find 78².
20. 20.Use (a + b)² = a² + 2ab + b² to find 12².
21. 21.Find the value of x² − 2xy + y² when x = 5 and y = 4.
22. 22.Find the value of x² − 2xy + y² when x = 9 and y = 3.
23. 23.Use a² − b² = (a + b)(a − b) to find 43² − 29².
24. 24.Find the value of x² − y² when x = 6 and y = 1.
25. 25.Use a² − b² = (a + b)(a − b) to find 97² − 79².
26. 26.Find the value of x² − y² when x = 13 and y = 2.
27. 27.Use (a + b)² = a² + 2ab + b² to find 31².
28. 28.Use a² − b² = (a + b)(a − b) to find 90² − 54².
29. 29.Use (a − b)² = a² − 2ab + b² to find 91².
30. 30.Use (a + b)² = a² + 2ab + b² to find 28².
31. 31.Use (a − b)² = a² − 2ab + b² to find 36².
32. 32.Use (a + b)² = a² + 2ab + b² to find 89².
33. 33.Find the value of x² − y² when x = 9 and y = 6.
34. 34.Use (a + b)(a − b) = a² − b² to find 21 × 19.
35. 35.Use (a + b)(a − b) = a² − b² to find 88 × 72.
36. 36.Use (a + b)² = a² + 2ab + b² to find 101².
37. 37.If a + b = 16 and ab = 60, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 41².
39. 39.Use (a + b)(a − b) = a² − b² to find 31 × 29.
40. 40.Use (a + b)(a − b) = a² − b² to find 107 × 93.

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