Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 856 · 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 71 × 69.
2. 2.Use (a − b)² = a² − 2ab + b² to find 49².
3. 3.Use (a + b)(a − b) = a² − b² to find 61 × 59.
4. 4.If a − b = 2 and ab = 3, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 101².
6. 6.Use (a − b)² = a² − 2ab + b² to find 57².
7. 7.Use a² − b² = (a + b)(a − b) to find 22² − 4².
8. 8.Use (a + b)(a − b) = a² − b² to find 26 × 14.
9. 9.Use (a + b)(a − b) = a² − b² to find 51 × 49.
10. 10.If a − b = 2 and ab = 48, what is a² + b²?
11. 11.If a + b = 4 and ab = 3, what is a² + b²?
12. 12.Use (a − b)² = a² − 2ab + b² to find 26².
13. 13.If a + b = 8 and ab = 12, what is a² + b²?
14. 14.If a − b = 3 and ab = 4, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 65².
16. 16.Use (a + b)(a − b) = a² − b² to find 77 × 63.
17. 17.Use (a − b)² = a² − 2ab + b² to find 42².
18. 18.If a − b = 1 and ab = 42, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 74².
20. 20.Use (a + b)² = a² + 2ab + b² to find 77².
21. 21.Use (a + b)(a − b) = a² − b² to find 39 × 21.
22. 22.If a − b = 6 and ab = 40, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 29 × 11.
24. 24.Use (a + b)(a − b) = a² − b² to find 31 × 29.
25. 25.Find the value of x² − y² when x = 14 and y = 6.
26. 26.Use a² − b² = (a + b)(a − b) to find 66² − 34².
27. 27.If a + b = 14 and ab = 45, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 61² − 30².
29. 29.If a + b = 3 and ab = 2, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 81².
31. 31.Use (a + b)² = a² + 2ab + b² to find 103².
32. 32.Use (a − b)² = a² − 2ab + b² to find 41².
33. 33.Use a² − b² = (a + b)(a − b) to find 25² − 5².
34. 34.Use (a + b)² = a² + 2ab + b² to find 106².
35. 35.Use a² − b² = (a + b)(a − b) to find 54² − 40².
36. 36.Use (a + b)² = a² + 2ab + b² to find 69².
37. 37.Find the value of x² − 2xy + y² when x = 4 and y = 1.
38. 38.Find the value of x² − y² when x = 15 and y = 7.
39. 39.Find the value of x² + 2xy + y² when x = 3 and y = 1.
40. 40.Use (a − b)² = a² − 2ab + b² to find 17².

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