Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 265 · 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 73 × 67.
2. 2.Use (a + b)(a − b) = a² − b² to find 93 × 87.
3. 3.If a + b = 4 and ab = 3, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 37².
5. 5.If a + b = 8 and ab = 7, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 78².
7. 7.Use (a + b)² = a² + 2ab + b² to find 75².
8. 8.Use (a + b)² = a² + 2ab + b² to find 38².
9. 9.Use (a − b)² = a² − 2ab + b² to find 48².
10. 10.Use (a − b)² = a² − 2ab + b² to find 75².
11. 11.Use a² − b² = (a + b)(a − b) to find 82² − 17².
12. 12.Find the value of x² − 2xy + y² when x = 4 and y = 2.
13. 13.Use a² − b² = (a + b)(a − b) to find 86² − 44².
14. 14.Use (a − b)² = a² − 2ab + b² to find 52².
15. 15.If a − b = 10 and ab = 24, what is a² + b²?
16. 16.Find the value of x² + 2xy + y² when x = 8 and y = 3.
17. 17.Use (a − b)² = a² − 2ab + b² to find 49².
18. 18.Use (a − b)² = a² − 2ab + b² to find 41².
19. 19.Find the value of x² − 2xy + y² when x = 4 and y = 3.
20. 20.Use (a + b)² = a² + 2ab + b² to find 13².
21. 21.Use (a + b)² = a² + 2ab + b² to find 71².
22. 22.If a + b = 7 and ab = 6, what is a² + b²?
23. 23.Find the value of x² − 2xy + y² when x = 6 and y = 2.
24. 24.If a − b = 8 and ab = 9, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 71² − 42².
26. 26.Use (a − b)² = a² − 2ab + b² to find 35².
27. 27.Use (a + b)² = a² + 2ab + b² to find 32².
28. 28.Find the value of x² + 2xy + y² when x = 15 and y = 4.
29. 29.Use (a + b)² = a² + 2ab + b² to find 12².
30. 30.Use (a − b)² = a² − 2ab + b² to find 82².
31. 31.Use (a − b)² = a² − 2ab + b² to find 77².
32. 32.Use (a + b)(a − b) = a² − b² to find 96 × 84.
33. 33.Use (a + b)² = a² + 2ab + b² to find 76².
34. 34.Use (a − b)² = a² − 2ab + b² to find 58².
35. 35.If a + b = 5 and ab = 6, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 107².
37. 37.Use (a + b)(a − b) = a² − b² to find 77 × 63.
38. 38.Use a² − b² = (a + b)(a − b) to find 44² − 28².
39. 39.Use (a − b)² = a² − 2ab + b² to find 43².
40. 40.Use (a − b)² = a² − 2ab + b² to find 14².

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