Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 431 · 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)² = a² − 2ab + b² to find 99².
2. 2.Find the value of x² − 2xy + y² when x = 14 and y = 7.
3. 3.Use a² − b² = (a + b)(a − b) to find 25² − 15².
4. 4.Use a² − b² = (a + b)(a − b) to find 75² − 63².
5. 5.If a + b = 13 and ab = 12, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 28².
7. 7.Use (a + b)(a − b) = a² − b² to find 65 × 55.
8. 8.Use (a + b)(a − b) = a² − b² to find 84 × 76.
9. 9.Use (a + b)(a − b) = a² − b² to find 54 × 46.
10. 10.Find the value of x² − 2xy + y² when x = 6 and y = 4.
11. 11.Use (a + b)(a − b) = a² − b² to find 73 × 67.
12. 12.Use (a + b)² = a² + 2ab + b² to find 89².
13. 13.If a + b = 15 and ab = 54, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 19².
15. 15.Use (a − b)² = a² − 2ab + b² to find 26².
16. 16.Use (a − b)² = a² − 2ab + b² to find 49².
17. 17.Find the value of x² + 2xy + y² when x = 6 and y = 5.
18. 18.Use (a − b)² = a² − 2ab + b² to find 87².
19. 19.If a − b = 4 and ab = 45, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 95².
21. 21.Use (a + b)² = a² + 2ab + b² to find 79².
22. 22.If a + b = 7 and ab = 10, what is a² + b²?
23. 23.Use (a + b)² = a² + 2ab + b² to find 108².
24. 24.Use (a + b)(a − b) = a² − b² to find 44 × 36.
25. 25.Use a² − b² = (a + b)(a − b) to find 35² − 18².
26. 26.Use a² − b² = (a + b)(a − b) to find 67² − 55².
27. 27.Use (a + b)² = a² + 2ab + b² to find 101².
28. 28.Use (a + b)² = a² + 2ab + b² to find 97².
29. 29.Use (a + b)² = a² + 2ab + b² to find 93².
30. 30.Use a² − b² = (a + b)(a − b) to find 89² − 84².
31. 31.Use a² − b² = (a + b)(a − b) to find 40² − 9².
32. 32.Find the value of x² + 2xy + y² when x = 3 and y = 1.
33. 33.Use a² − b² = (a + b)(a − b) to find 64² − 46².
34. 34.Use (a − b)² = a² − 2ab + b² to find 29².
35. 35.Use (a + b)² = a² + 2ab + b² to find 51².
36. 36.Use a² − b² = (a + b)(a − b) to find 55² − 8².
37. 37.Use a² − b² = (a + b)(a − b) to find 80² − 41².
38. 38.Find the value of x² − y² when x = 7 and y = 6.
39. 39.Use (a + b)² = a² + 2ab + b² to find 67².
40. 40.Use (a + b)² = a² + 2ab + b² to find 58².

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