Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 628 · 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)² = a² − 2ab + b² to find 94².
2. 2.Use (a + b)(a − b) = a² − b² to find 105 × 95.
3. 3.Use a² − b² = (a + b)(a − b) to find 30² − 27².
4. 4.If a + b = 18 and ab = 72, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 49².
6. 6.Use (a + b)(a − b) = a² − b² to find 51 × 49.
7. 7.Use a² − b² = (a + b)(a − b) to find 24² − 22².
8. 8.Use (a − b)² = a² − 2ab + b² to find 74².
9. 9.If a + b = 15 and ab = 50, what is a² + b²?
10. 10.Use (a + b)(a − b) = a² − b² to find 38 × 22.
11. 11.Use (a + b)² = a² + 2ab + b² to find 27².
12. 12.Use (a + b)² = a² + 2ab + b² to find 95².
13. 13.Use (a − b)² = a² − 2ab + b² to find 88².
14. 14.Use (a + b)(a − b) = a² − b² to find 57 × 43.
15. 15.If a + b = 6 and ab = 5, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 86² − 19².
17. 17.Use (a + b)² = a² + 2ab + b² to find 45².
18. 18.Use a² − b² = (a + b)(a − b) to find 71² − 42².
19. 19.Use (a − b)² = a² − 2ab + b² to find 43².
20. 20.Use (a − b)² = a² − 2ab + b² to find 47².
21. 21.Use (a + b)(a − b) = a² − b² to find 47 × 33.
22. 22.If a − b = 4 and ab = 5, what is a² + b²?
23. 23.Use (a + b)² = a² + 2ab + b² to find 29².
24. 24.Find the value of x² + 2xy + y² when x = 3 and y = 2.
25. 25.Use (a + b)(a − b) = a² − b² to find 23 × 17.
26. 26.If a + b = 11 and ab = 10, what is a² + b²?
27. 27.If a − b = 1 and ab = 12, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 39².
29. 29.Use (a − b)² = a² − 2ab + b² to find 83².
30. 30.Use a² − b² = (a + b)(a − b) to find 42² − 31².
31. 31.Use (a − b)² = a² − 2ab + b² to find 13².
32. 32.Use (a − b)² = a² − 2ab + b² to find 59².
33. 33.Find the value of x² − y² when x = 15 and y = 6.
34. 34.Use (a − b)² = a² − 2ab + b² to find 14².
35. 35.Use (a − b)² = a² − 2ab + b² to find 56².
36. 36.If a − b = 10 and ab = 11, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 94 × 86.
38. 38.If a − b = 8 and ab = 33, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 12².
40. 40.Find the value of x² + 2xy + y² when x = 4 and y = 1.

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