Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 372 · 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.Find the value of x² − y² when x = 7 and y = 2.
2. 2.Use (a − b)² = a² − 2ab + b² to find 47².
3. 3.Find the value of x² − 2xy + y² when x = 11 and y = 3.
4. 4.Use a² − b² = (a + b)(a − b) to find 37² − 16².
5. 5.Use (a + b)(a − b) = a² − b² to find 94 × 86.
6. 6.Use a² − b² = (a + b)(a − b) to find 75² − 35².
7. 7.Use (a + b)² = a² + 2ab + b² to find 32².
8. 8.If a + b = 9 and ab = 18, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 22².
10. 10.Use a² − b² = (a + b)(a − b) to find 37² − 4².
11. 11.Use (a + b)² = a² + 2ab + b² to find 28².
12. 12.Use (a − b)² = a² − 2ab + b² to find 81².
13. 13.Use a² − b² = (a + b)(a − b) to find 60² − 18².
14. 14.Find the value of x² + 2xy + y² when x = 14 and y = 3.
15. 15.Use (a − b)² = a² − 2ab + b² to find 33².
16. 16.Use (a + b)² = a² + 2ab + b² to find 87².
17. 17.If a + b = 9 and ab = 14, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 96².
19. 19.Use (a + b)(a − b) = a² − b² to find 58 × 42.
20. 20.Use (a + b)(a − b) = a² − b² to find 62 × 58.
21. 21.Use (a − b)² = a² − 2ab + b² to find 13².
22. 22.Use (a + b)(a − b) = a² − b² to find 75 × 65.
23. 23.Use a² − b² = (a + b)(a − b) to find 76² − 50².
24. 24.If a − b = 2 and ab = 3, what is a² + b²?
25. 25.Find the value of x² − y² when x = 5 and y = 1.
26. 26.Use a² − b² = (a + b)(a − b) to find 79² − 12².
27. 27.Use (a + b)(a − b) = a² − b² to find 86 × 74.
28. 28.Find the value of x² + 2xy + y² when x = 6 and y = 1.
29. 29.Use a² − b² = (a + b)(a − b) to find 54² − 33².
30. 30.Use (a + b)(a − b) = a² − b² to find 79 × 61.
31. 31.If a + b = 6 and ab = 5, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 16².
33. 33.Use (a + b)(a − b) = a² − b² to find 91 × 89.
34. 34.Use a² − b² = (a + b)(a − b) to find 35² − 34².
35. 35.Find the value of x² − y² when x = 12 and y = 6.
36. 36.Use (a − b)² = a² − 2ab + b² to find 43².
37. 37.Use (a − b)² = a² − 2ab + b² to find 18².
38. 38.Use a² − b² = (a + b)(a − b) to find 35² − 33².
39. 39.If a − b = 7 and ab = 30, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 39².

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