Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 203 · 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 84 × 76.
2. 2.Use (a + b)² = a² + 2ab + b² to find 19².
3. 3.Use (a − b)² = a² − 2ab + b² to find 97².
4. 4.Use (a + b)² = a² + 2ab + b² to find 23².
5. 5.Use a² − b² = (a + b)(a − b) to find 84² − 45².
6. 6.Use (a + b)(a − b) = a² − b² to find 63 × 57.
7. 7.If a − b = 3 and ab = 108, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 25².
9. 9.Use (a + b)(a − b) = a² − b² to find 88 × 72.
10. 10.Use a² − b² = (a + b)(a − b) to find 86² − 2².
11. 11.Use (a − b)² = a² − 2ab + b² to find 35².
12. 12.Use (a + b)² = a² + 2ab + b² to find 14².
13. 13.Use (a + b)² = a² + 2ab + b² to find 94².
14. 14.Use (a + b)(a − b) = a² − b² to find 46 × 34.
15. 15.If a + b = 3 and ab = 2, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 41².
17. 17.Use (a + b)² = a² + 2ab + b² to find 49².
18. 18.Find the value of x² − y² when x = 4 and y = 1.
19. 19.Use (a − b)² = a² − 2ab + b² to find 67².
20. 20.Use (a + b)(a − b) = a² − b² to find 32 × 28.
21. 21.Use a² − b² = (a + b)(a − b) to find 62² − 24².
22. 22.Use (a − b)² = a² − 2ab + b² to find 95².
23. 23.Use (a − b)² = a² − 2ab + b² to find 15².
24. 24.If a + b = 10 and ab = 16, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 49².
26. 26.Find the value of x² − 2xy + y² when x = 6 and y = 4.
27. 27.Use (a + b)² = a² + 2ab + b² to find 46².
28. 28.If a − b = 10 and ab = 11, what is a² + b²?
29. 29.If a − b = 2 and ab = 120, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 26² − 14².
31. 31.Use (a + b)(a − b) = a² − b² to find 35 × 25.
32. 32.Use (a + b)(a − b) = a² − b² to find 106 × 94.
33. 33.If a + b = 11 and ab = 30, what is a² + b²?
34. 34.Use a² − b² = (a + b)(a − b) to find 81² − 68².
35. 35.Use (a + b)(a − b) = a² − b² to find 38 × 22.
36. 36.Use (a + b)(a − b) = a² − b² to find 81 × 79.
37. 37.Use (a + b)(a − b) = a² − b² to find 47 × 33.
38. 38.Use (a − b)² = a² − 2ab + b² to find 36².
39. 39.Use (a + b)(a − b) = a² − b² to find 27 × 13.
40. 40.Use (a + b)² = a² + 2ab + b² to find 72².

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