Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 669 · 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 + 2xy + y² when x = 8 and y = 2.
2. 2.If a − b = 3 and ab = 10, what is a² + b²?
3. 3.If a + b = 9 and ab = 14, what is a² + b²?
4. 4.Use (a + b)(a − b) = a² − b² to find 31 × 29.
5. 5.Use (a + b)(a − b) = a² − b² to find 101 × 99.
6. 6.If a + b = 10 and ab = 9, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 94².
8. 8.Use (a + b)² = a² + 2ab + b² to find 71².
9. 9.Use (a + b)(a − b) = a² − b² to find 67 × 53.
10. 10.Use (a − b)² = a² − 2ab + b² to find 71².
11. 11.If a − b = 2 and ab = 3, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 61² − 35².
13. 13.Use (a + b)² = a² + 2ab + b² to find 41².
14. 14.Use (a + b)² = a² + 2ab + b² to find 99².
15. 15.Use (a − b)² = a² − 2ab + b² to find 68².
16. 16.Use (a + b)² = a² + 2ab + b² to find 37².
17. 17.Find the value of x² + 2xy + y² when x = 12 and y = 11.
18. 18.If a − b = 3 and ab = 88, what is a² + b²?
19. 19.Find the value of x² − 2xy + y² when x = 15 and y = 10.
20. 20.Use a² − b² = (a + b)(a − b) to find 88² − 18².
21. 21.Use a² − b² = (a + b)(a − b) to find 59² − 14².
22. 22.Use a² − b² = (a + b)(a − b) to find 87² − 12².
23. 23.Use (a + b)(a − b) = a² − b² to find 64 × 56.
24. 24.Use a² − b² = (a + b)(a − b) to find 90² − 48².
25. 25.Use (a − b)² = a² − 2ab + b² to find 49².
26. 26.If a + b = 12 and ab = 20, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 13².
28. 28.Find the value of x² − y² when x = 11 and y = 10.
29. 29.Use (a + b)² = a² + 2ab + b² to find 86².
30. 30.If a + b = 13 and ab = 12, what is a² + b²?
31. 31.Use (a − b)² = a² − 2ab + b² to find 26².
32. 32.Use a² − b² = (a + b)(a − b) to find 31² − 25².
33. 33.Use a² − b² = (a + b)(a − b) to find 91² − 8².
34. 34.Find the value of x² + 2xy + y² when x = 12 and y = 4.
35. 35.Use (a − b)² = a² − 2ab + b² to find 43².
36. 36.Use (a + b)(a − b) = a² − b² to find 61 × 59.
37. 37.Use a² − b² = (a + b)(a − b) to find 27² − 18².
38. 38.Use (a + b)(a − b) = a² − b² to find 93 × 87.
39. 39.Use (a − b)² = a² − 2ab + b² to find 95².
40. 40.Use (a + b)(a − b) = a² − b² to find 104 × 96.

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