Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 69 · 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 53².
2. 2.Find the value of x² + 2xy + y² when x = 14 and y = 4.
3. 3.If a + b = 11 and ab = 18, what is a² + b²?
4. 4.If a − b = 8 and ab = 9, what is a² + b²?
5. 5.If a − b = 8 and ab = 48, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 89 × 71.
7. 7.Use a² − b² = (a + b)(a − b) to find 51² − 26².
8. 8.Use (a + b)(a − b) = a² − b² to find 99 × 81.
9. 9.Use (a + b)(a − b) = a² − b² to find 45 × 35.
10. 10.Find the value of x² − y² when x = 13 and y = 4.
11. 11.Use (a + b)(a − b) = a² − b² to find 41 × 39.
12. 12.Use (a + b)² = a² + 2ab + b² to find 47².
13. 13.Find the value of x² − y² when x = 9 and y = 2.
14. 14.Use a² − b² = (a + b)(a − b) to find 99² − 91².
15. 15.Use (a + b)² = a² + 2ab + b² to find 57².
16. 16.Use (a + b)² = a² + 2ab + b² to find 61².
17. 17.Use (a − b)² = a² − 2ab + b² to find 52².
18. 18.Use (a − b)² = a² − 2ab + b² to find 63².
19. 19.Use (a + b)(a − b) = a² − b² to find 95 × 85.
20. 20.Use (a + b)(a − b) = a² − b² to find 58 × 42.
21. 21.Use (a − b)² = a² − 2ab + b² to find 18².
22. 22.Use (a + b)² = a² + 2ab + b² to find 96².
23. 23.Use (a + b)² = a² + 2ab + b² to find 91².
24. 24.Use (a + b)² = a² + 2ab + b² to find 104².
25. 25.Use (a − b)² = a² − 2ab + b² to find 99².
26. 26.Find the value of x² + 2xy + y² when x = 8 and y = 2.
27. 27.Use (a + b)(a − b) = a² − b² to find 54 × 46.
28. 28.If a + b = 3 and ab = 2, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 41².
30. 30.Use (a + b)² = a² + 2ab + b² to find 79².
31. 31.Use a² − b² = (a + b)(a − b) to find 57² − 3².
32. 32.Find the value of x² − y² when x = 8 and y = 5.
33. 33.If a − b = 1 and ab = 6, what is a² + b²?
34. 34.Find the value of x² − y² when x = 10 and y = 1.
35. 35.Find the value of x² − y² when x = 6 and y = 3.
36. 36.Use (a + b)(a − b) = a² − b² to find 53 × 47.
37. 37.Use (a + b)(a − b) = a² − b² to find 52 × 48.
38. 38.Use (a + b)² = a² + 2ab + b² to find 89².
39. 39.Use a² − b² = (a + b)(a − b) to find 34² − 18².
40. 40.Use (a − b)² = a² − 2ab + b² to find 58².

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