Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 486 · 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.Use (a + b)(a − b) = a² − b² to find 26 × 14.
2. 2.Use a² − b² = (a + b)(a − b) to find 52² − 50².
3. 3.Use a² − b² = (a + b)(a − b) to find 63² − 36².
4. 4.If a − b = 2 and ab = 3, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 23².
6. 6.Use (a − b)² = a² − 2ab + b² to find 37².
7. 7.Find the value of x² − y² when x = 11 and y = 10.
8. 8.Use (a − b)² = a² − 2ab + b² to find 57².
9. 9.Use (a + b)(a − b) = a² − b² to find 87 × 73.
10. 10.Find the value of x² − y² when x = 9 and y = 8.
11. 11.Use a² − b² = (a + b)(a − b) to find 86² − 66².
12. 12.If a + b = 13 and ab = 42, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 45² − 17².
14. 14.Use (a − b)² = a² − 2ab + b² to find 65².
15. 15.Use (a − b)² = a² − 2ab + b² to find 89².
16. 16.If a − b = 1 and ab = 12, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 18².
18. 18.Use (a + b)(a − b) = a² − b² to find 104 × 96.
19. 19.Use a² − b² = (a + b)(a − b) to find 72² − 67².
20. 20.Find the value of x² + 2xy + y² when x = 9 and y = 2.
21. 21.Use (a + b)² = a² + 2ab + b² to find 51².
22. 22.Use (a + b)(a − b) = a² − b² to find 41 × 39.
23. 23.Find the value of x² − y² when x = 4 and y = 3.
24. 24.Use a² − b² = (a + b)(a − b) to find 96² − 65².
25. 25.If a − b = 4 and ab = 32, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 98² − 10².
27. 27.Use a² − b² = (a + b)(a − b) to find 45² − 33².
28. 28.Find the value of x² − 2xy + y² when x = 9 and y = 5.
29. 29.If a + b = 13 and ab = 30, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 15².
31. 31.Use (a − b)² = a² − 2ab + b² to find 25².
32. 32.If a + b = 5 and ab = 4, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 92².
34. 34.Use (a + b)(a − b) = a² − b² to find 53 × 47.
35. 35.Use (a + b)² = a² + 2ab + b² to find 101².
36. 36.If a − b = 2 and ab = 24, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 17².
38. 38.Use (a − b)² = a² − 2ab + b² to find 52².
39. 39.Use a² − b² = (a + b)(a − b) to find 69² − 28².
40. 40.Use (a + b)² = a² + 2ab + b² to find 12².

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