Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 65 · 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.If a + b = 7 and ab = 10, what is a² + b²?
2. 2.Find the value of x² − 2xy + y² when x = 6 and y = 2.
3. 3.Use (a + b)(a − b) = a² − b² to find 86 × 74.
4. 4.Use a² − b² = (a + b)(a − b) to find 83² − 71².
5. 5.Use (a − b)² = a² − 2ab + b² to find 26².
6. 6.Use (a + b)(a − b) = a² − b² to find 84 × 76.
7. 7.Use a² − b² = (a + b)(a − b) to find 69² − 48².
8. 8.Find the value of x² − 2xy + y² when x = 10 and y = 1.
9. 9.Use (a + b)(a − b) = a² − b² to find 45 × 35.
10. 10.Use a² − b² = (a + b)(a − b) to find 40² − 9².
11. 11.Find the value of x² − y² when x = 10 and y = 9.
12. 12.Use (a − b)² = a² − 2ab + b² to find 36².
13. 13.If a + b = 7 and ab = 12, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 43 × 37.
15. 15.Use (a + b)² = a² + 2ab + b² to find 14².
16. 16.If a + b = 6 and ab = 5, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 18².
18. 18.Find the value of x² − 2xy + y² when x = 10 and y = 4.
19. 19.Use (a + b)² = a² + 2ab + b² to find 49².
20. 20.Use (a − b)² = a² − 2ab + b² to find 48².
21. 21.Use (a + b)² = a² + 2ab + b² to find 101².
22. 22.Use (a + b)² = a² + 2ab + b² to find 43².
23. 23.If a − b = 8 and ab = 33, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 42².
25. 25.Use (a + b)² = a² + 2ab + b² to find 37².
26. 26.If a − b = 2 and ab = 35, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 75² − 24².
28. 28.Use (a + b)(a − b) = a² − b² to find 38 × 22.
29. 29.Find the value of x² − y² when x = 9 and y = 2.
30. 30.If a + b = 13 and ab = 40, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 63² − 42².
32. 32.Use (a − b)² = a² − 2ab + b² to find 34².
33. 33.Use (a + b)² = a² + 2ab + b² to find 34².
34. 34.Find the value of x² + 2xy + y² when x = 6 and y = 1.
35. 35.Use (a − b)² = a² − 2ab + b² to find 21².
36. 36.Find the value of x² + 2xy + y² when x = 6 and y = 3.
37. 37.Use (a − b)² = a² − 2ab + b² to find 94².
38. 38.Use (a − b)² = a² − 2ab + b² to find 58².
39. 39.Use (a + b)² = a² + 2ab + b² to find 71².
40. 40.Use a² − b² = (a + b)(a − b) to find 73² − 19².

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