Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 38 · 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 12².
2. 2.Use (a + b)(a − b) = a² − b² to find 45 × 35.
3. 3.If a + b = 10 and ab = 24, what is a² + b²?
4. 4.Use a² − b² = (a + b)(a − b) to find 74² − 66².
5. 5.Use (a − b)² = a² − 2ab + b² to find 61².
6. 6.Use (a + b)(a − b) = a² − b² to find 33 × 27.
7. 7.Use (a − b)² = a² − 2ab + b² to find 18².
8. 8.Use (a − b)² = a² − 2ab + b² to find 22².
9. 9.If a + b = 10 and ab = 9, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 25² − 10².
11. 11.If a − b = 4 and ab = 5, what is a² + b²?
12. 12.Use (a − b)² = a² − 2ab + b² to find 37².
13. 13.Use (a + b)² = a² + 2ab + b² to find 52².
14. 14.Use (a − b)² = a² − 2ab + b² to find 39².
15. 15.Use (a + b)(a − b) = a² − b² to find 55 × 45.
16. 16.Use (a − b)² = a² − 2ab + b² to find 15².
17. 17.Use (a + b)² = a² + 2ab + b² to find 23².
18. 18.Use (a + b)² = a² + 2ab + b² to find 104².
19. 19.Use (a − b)² = a² − 2ab + b² to find 88².
20. 20.Use a² − b² = (a + b)(a − b) to find 23² − 22².
21. 21.Use a² − b² = (a + b)(a − b) to find 94² − 20².
22. 22.Find the value of x² − 2xy + y² when x = 3 and y = 2.
23. 23.Use (a + b)(a − b) = a² − b² to find 78 × 62.
24. 24.Use (a − b)² = a² − 2ab + b² to find 62².
25. 25.Find the value of x² + 2xy + y² when x = 3 and y = 1.
26. 26.If a + b = 5 and ab = 6, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 52 × 48.
28. 28.Use a² − b² = (a + b)(a − b) to find 48² − 12².
29. 29.Use (a − b)² = a² − 2ab + b² to find 38².
30. 30.Use a² − b² = (a + b)(a − b) to find 91² − 12².
31. 31.Use (a + b)(a − b) = a² − b² to find 108 × 92.
32. 32.Use (a − b)² = a² − 2ab + b² to find 45².
33. 33.Use (a + b)² = a² + 2ab + b² to find 16².
34. 34.Use (a + b)² = a² + 2ab + b² to find 41².
35. 35.Use (a − b)² = a² − 2ab + b² to find 52².
36. 36.Use (a + b)² = a² + 2ab + b² to find 78².
37. 37.Use a² − b² = (a + b)(a − b) to find 87² − 40².
38. 38.Find the value of x² − 2xy + y² when x = 6 and y = 2.
39. 39.Find the value of x² + 2xy + y² when x = 3 and y = 2.
40. 40.Use (a + b)² = a² + 2ab + b² to find 71².

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