Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 640 · 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 103 × 97.
2. 2.If a − b = 2 and ab = 3, what is a² + b²?
3. 3.If a − b = 11 and ab = 12, what is a² + b²?
4. 4.Use a² − b² = (a + b)(a − b) to find 26² − 10².
5. 5.Use a² − b² = (a + b)(a − b) to find 77² − 64².
6. 6.Use (a + b)² = a² + 2ab + b² to find 49².
7. 7.Use a² − b² = (a + b)(a − b) to find 21² − 1².
8. 8.Use (a − b)² = a² − 2ab + b² to find 26².
9. 9.Use (a − b)² = a² − 2ab + b² to find 28².
10. 10.If a − b = 6 and ab = 16, what is a² + b²?
11. 11.Find the value of x² − 2xy + y² when x = 9 and y = 7.
12. 12.Use a² − b² = (a + b)(a − b) to find 66² − 17².
13. 13.Use a² − b² = (a + b)(a − b) to find 69² − 50².
14. 14.Find the value of x² + 2xy + y² when x = 15 and y = 3.
15. 15.Find the value of x² − 2xy + y² when x = 3 and y = 1.
16. 16.Find the value of x² + 2xy + y² when x = 11 and y = 6.
17. 17.Use (a + b)² = a² + 2ab + b² to find 97².
18. 18.Find the value of x² − y² when x = 14 and y = 7.
19. 19.Use a² − b² = (a + b)(a − b) to find 70² − 63².
20. 20.If a − b = 7 and ab = 8, what is a² + b²?
21. 21.Use (a + b)² = a² + 2ab + b² to find 101².
22. 22.Use (a − b)² = a² − 2ab + b² to find 64².
23. 23.Use (a + b)² = a² + 2ab + b² to find 14².
24. 24.Use (a − b)² = a² − 2ab + b² to find 48².
25. 25.Use (a + b)(a − b) = a² − b² to find 97 × 83.
26. 26.Use (a + b)(a − b) = a² − b² to find 74 × 66.
27. 27.Use (a + b)(a − b) = a² − b² to find 29 × 11.
28. 28.Use (a + b)(a − b) = a² − b² to find 35 × 25.
29. 29.If a + b = 3 and ab = 2, what is a² + b²?
30. 30.If a − b = 2 and ab = 99, what is a² + b²?
31. 31.Find the value of x² − y² when x = 4 and y = 3.
32. 32.Use (a − b)² = a² − 2ab + b² to find 83².
33. 33.Use (a + b)² = a² + 2ab + b² to find 59².
34. 34.Use (a + b)(a − b) = a² − b² to find 42 × 38.
35. 35.Use a² − b² = (a + b)(a − b) to find 80² − 13².
36. 36.Use (a − b)² = a² − 2ab + b² to find 41².
37. 37.If a − b = 3 and ab = 54, what is a² + b²?
38. 38.Use a² − b² = (a + b)(a − b) to find 84² − 37².
39. 39.Use (a + b)(a − b) = a² − b² to find 71 × 69.
40. 40.Use (a + b)(a − b) = a² − b² to find 104 × 96.

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