Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 764 · 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 = 10 and ab = 24, what is a² + b²?
2. 2.Find the value of x² + 2xy + y² when x = 3 and y = 1.
3. 3.Use (a − b)² = a² − 2ab + b² to find 49².
4. 4.Use (a − b)² = a² − 2ab + b² to find 25².
5. 5.Use (a + b)(a − b) = a² − b² to find 56 × 44.
6. 6.If a − b = 5 and ab = 14, what is a² + b²?
7. 7.If a + b = 4 and ab = 3, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 22².
9. 9.Use (a + b)(a − b) = a² − b² to find 79 × 61.
10. 10.Use (a − b)² = a² − 2ab + b² to find 65².
11. 11.Find the value of x² − y² when x = 11 and y = 2.
12. 12.Use a² − b² = (a + b)(a − b) to find 33² − 5².
13. 13.Use (a − b)² = a² − 2ab + b² to find 76².
14. 14.If a + b = 12 and ab = 20, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 42².
16. 16.Use (a + b)(a − b) = a² − b² to find 108 × 92.
17. 17.Find the value of x² − 2xy + y² when x = 6 and y = 5.
18. 18.Use (a + b)(a − b) = a² − b² to find 104 × 96.
19. 19.Use (a − b)² = a² − 2ab + b² to find 22².
20. 20.Use a² − b² = (a + b)(a − b) to find 76² − 1².
21. 21.Find the value of x² + 2xy + y² when x = 11 and y = 5.
22. 22.Use (a + b)(a − b) = a² − b² to find 58 × 42.
23. 23.Use (a + b)² = a² + 2ab + b² to find 88².
24. 24.Find the value of x² − y² when x = 11 and y = 10.
25. 25.Use (a + b)(a − b) = a² − b² to find 81 × 79.
26. 26.If a − b = 7 and ab = 44, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 55².
28. 28.Use (a + b)² = a² + 2ab + b² to find 82².
29. 29.Use (a + b)(a − b) = a² − b² to find 39 × 21.
30. 30.Use a² − b² = (a + b)(a − b) to find 83² − 71².
31. 31.If a + b = 14 and ab = 40, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 66².
33. 33.Use (a + b)² = a² + 2ab + b² to find 67².
34. 34.Find the value of x² + 2xy + y² when x = 5 and y = 2.
35. 35.Use (a + b)(a − b) = a² − b² to find 99 × 81.
36. 36.Use a² − b² = (a + b)(a − b) to find 54² − 4².
37. 37.Use (a + b)² = a² + 2ab + b² to find 31².
38. 38.If a − b = 2 and ab = 48, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 16².
40. 40.If a − b = 1 and ab = 72, what is a² + b²?

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