Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 352 · 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 87².
2. 2.If a + b = 15 and ab = 44, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 23².
4. 4.If a − b = 2 and ab = 3, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 25².
6. 6.Use (a + b)² = a² + 2ab + b² to find 27².
7. 7.Find the value of x² + 2xy + y² when x = 7 and y = 5.
8. 8.Find the value of x² − 2xy + y² when x = 14 and y = 13.
9. 9.Find the value of x² − 2xy + y² when x = 6 and y = 4.
10. 10.Use (a + b)² = a² + 2ab + b² to find 71².
11. 11.Use (a + b)(a − b) = a² − b² to find 65 × 55.
12. 12.Use (a + b)² = a² + 2ab + b² to find 29².
13. 13.If a − b = 1 and ab = 6, what is a² + b²?
14. 14.Find the value of x² − y² when x = 6 and y = 2.
15. 15.Use (a − b)² = a² − 2ab + b² to find 16².
16. 16.Use (a + b)(a − b) = a² − b² to find 62 × 58.
17. 17.Use a² − b² = (a + b)(a − b) to find 46² − 6².
18. 18.Find the value of x² + 2xy + y² when x = 12 and y = 7.
19. 19.Use (a − b)² = a² − 2ab + b² to find 65².
20. 20.Use a² − b² = (a + b)(a − b) to find 58² − 40².
21. 21.If a + b = 6 and ab = 8, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 71².
23. 23.If a + b = 14 and ab = 48, what is a² + b²?
24. 24.Use (a + b)² = a² + 2ab + b² to find 72².
25. 25.Use a² − b² = (a + b)(a − b) to find 83² − 6².
26. 26.Use (a + b)² = a² + 2ab + b² to find 34².
27. 27.Use (a + b)² = a² + 2ab + b² to find 15².
28. 28.If a + b = 22 and ab = 120, what is a² + b²?
29. 29.If a − b = 4 and ab = 5, what is a² + b²?
30. 30.Find the value of x² − 2xy + y² when x = 6 and y = 3.
31. 31.Use a² − b² = (a + b)(a − b) to find 27² − 4².
32. 32.Use (a + b)² = a² + 2ab + b² to find 66².
33. 33.If a − b = 3 and ab = 10, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 25 × 15.
35. 35.Use (a + b)(a − b) = a² − b² to find 46 × 34.
36. 36.Find the value of x² − y² when x = 10 and y = 2.
37. 37.Use (a + b)(a − b) = a² − b² to find 98 × 82.
38. 38.Use a² − b² = (a + b)(a − b) to find 20² − 10².
39. 39.Find the value of x² − y² when x = 13 and y = 2.
40. 40.Use (a − b)² = a² − 2ab + b² to find 56².

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