Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 155 · 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 97 × 83.
2. 2.Use (a − b)² = a² − 2ab + b² to find 83².
3. 3.Use a² − b² = (a + b)(a − b) to find 71² − 23².
4. 4.Use a² − b² = (a + b)(a − b) to find 89² − 31².
5. 5.Use (a + b)² = a² + 2ab + b² to find 71².
6. 6.Use (a + b)(a − b) = a² − b² to find 62 × 58.
7. 7.If a − b = 3 and ab = 108, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 84² − 60².
9. 9.If a + b = 6 and ab = 8, what is a² + b²?
10. 10.Use (a + b)(a − b) = a² − b² to find 43 × 37.
11. 11.Use (a − b)² = a² − 2ab + b² to find 68².
12. 12.If a + b = 13 and ab = 30, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 95².
14. 14.Use (a + b)² = a² + 2ab + b² to find 81².
15. 15.Find the value of x² − y² when x = 10 and y = 7.
16. 16.Find the value of x² − 2xy + y² when x = 6 and y = 4.
17. 17.Use (a − b)² = a² − 2ab + b² to find 16².
18. 18.Use (a + b)(a − b) = a² − b² to find 76 × 64.
19. 19.Use (a + b)² = a² + 2ab + b² to find 39².
20. 20.Use (a + b)(a − b) = a² − b² to find 59 × 41.
21. 21.If a + b = 9 and ab = 20, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 97².
23. 23.Use (a + b)² = a² + 2ab + b² to find 37².
24. 24.Use (a − b)² = a² − 2ab + b² to find 81².
25. 25.Use (a + b)(a − b) = a² − b² to find 86 × 74.
26. 26.Use (a + b)² = a² + 2ab + b² to find 54².
27. 27.Use (a − b)² = a² − 2ab + b² to find 14².
28. 28.Use (a + b)(a − b) = a² − b² to find 29 × 11.
29. 29.Use (a + b)(a − b) = a² − b² to find 99 × 81.
30. 30.Use (a + b)² = a² + 2ab + b² to find 62².
31. 31.Find the value of x² + 2xy + y² when x = 12 and y = 1.
32. 32.Use (a − b)² = a² − 2ab + b² to find 27².
33. 33.Use (a − b)² = a² − 2ab + b² to find 84².
34. 34.Find the value of x² − y² when x = 10 and y = 2.
35. 35.Use (a + b)(a − b) = a² − b² to find 94 × 86.
36. 36.If a + b = 23 and ab = 132, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 27 × 13.
38. 38.Use (a + b)(a − b) = a² − b² to find 106 × 94.
39. 39.Use (a + b)² = a² + 2ab + b² to find 18².
40. 40.Use (a − b)² = a² − 2ab + b² to find 46².

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