Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 937 · 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 = 3 and ab = 4, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 28².
3. 3.Use (a − b)² = a² − 2ab + b² to find 75².
4. 4.Use (a + b)(a − b) = a² − b² to find 21 × 19.
5. 5.Use a² − b² = (a + b)(a − b) to find 44² − 7².
6. 6.Use (a − b)² = a² − 2ab + b² to find 42².
7. 7.Use a² − b² = (a + b)(a − b) to find 67² − 16².
8. 8.Use (a + b)(a − b) = a² − b² to find 63 × 57.
9. 9.Use (a − b)² = a² − 2ab + b² to find 34².
10. 10.Find the value of x² + 2xy + y² when x = 5 and y = 1.
11. 11.Use (a + b)² = a² + 2ab + b² to find 59².
12. 12.Use (a + b)² = a² + 2ab + b² to find 37².
13. 13.If a − b = 4 and ab = 77, what is a² + b²?
14. 14.Find the value of x² + 2xy + y² when x = 7 and y = 4.
15. 15.Find the value of x² + 2xy + y² when x = 9 and y = 5.
16. 16.Use a² − b² = (a + b)(a − b) to find 59² − 8².
17. 17.Use a² − b² = (a + b)(a − b) to find 94² − 11².
18. 18.Use a² − b² = (a + b)(a − b) to find 90² − 63².
19. 19.Use (a − b)² = a² − 2ab + b² to find 82².
20. 20.Use a² − b² = (a + b)(a − b) to find 93² − 27².
21. 21.Find the value of x² − 2xy + y² when x = 14 and y = 2.
22. 22.Use (a + b)(a − b) = a² − b² to find 66 × 54.
23. 23.Use (a − b)² = a² − 2ab + b² to find 36².
24. 24.Use a² − b² = (a + b)(a − b) to find 20² − 8².
25. 25.If a + b = 3 and ab = 2, what is a² + b²?
26. 26.If a − b = 3 and ab = 28, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 65².
28. 28.Use (a + b)(a − b) = a² − b² to find 91 × 89.
29. 29.Use (a + b)² = a² + 2ab + b² to find 89².
30. 30.Find the value of x² − 2xy + y² when x = 7 and y = 3.
31. 31.Use (a + b)(a − b) = a² − b² to find 92 × 88.
32. 32.Use a² − b² = (a + b)(a − b) to find 25² − 2².
33. 33.Use a² − b² = (a + b)(a − b) to find 30² − 18².
34. 34.If a − b = 1 and ab = 2, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 68².
36. 36.Use (a + b)(a − b) = a² − b² to find 48 × 32.
37. 37.Use (a + b)² = a² + 2ab + b² to find 14².
38. 38.Use (a + b)(a − b) = a² − b² to find 37 × 23.
39. 39.Use (a − b)² = a² − 2ab + b² to find 19².
40. 40.Use (a + b)(a − b) = a² − b² to find 42 × 38.

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