Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 367 · 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 35².
2. 2.Use (a + b)² = a² + 2ab + b² to find 92².
3. 3.Use (a − b)² = a² − 2ab + b² to find 42².
4. 4.If a + b = 9 and ab = 8, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 73².
6. 6.Use (a + b)(a − b) = a² − b² to find 37 × 23.
7. 7.If a − b = 3 and ab = 10, what is a² + b²?
8. 8.If a − b = 8 and ab = 9, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 39² − 28².
10. 10.Use (a − b)² = a² − 2ab + b² to find 24².
11. 11.Find the value of x² + 2xy + y² when x = 3 and y = 1.
12. 12.Find the value of x² − y² when x = 11 and y = 6.
13. 13.Use a² − b² = (a + b)(a − b) to find 57² − 5².
14. 14.Find the value of x² + 2xy + y² when x = 6 and y = 1.
15. 15.Use (a − b)² = a² − 2ab + b² to find 82².
16. 16.Use a² − b² = (a + b)(a − b) to find 72² − 25².
17. 17.If a − b = 2 and ab = 8, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 96².
19. 19.Use (a + b)(a − b) = a² − b² to find 47 × 33.
20. 20.Use (a + b)² = a² + 2ab + b² to find 18².
21. 21.Use (a − b)² = a² − 2ab + b² to find 88².
22. 22.Use (a + b)² = a² + 2ab + b² to find 44².
23. 23.Use a² − b² = (a + b)(a − b) to find 96² − 72².
24. 24.Use (a − b)² = a² − 2ab + b² to find 15².
25. 25.Use a² − b² = (a + b)(a − b) to find 97² − 16².
26. 26.Use a² − b² = (a + b)(a − b) to find 39² − 3².
27. 27.Use (a + b)(a − b) = a² − b² to find 44 × 36.
28. 28.Use a² − b² = (a + b)(a − b) to find 28² − 22².
29. 29.Use (a + b)² = a² + 2ab + b² to find 32².
30. 30.Use (a + b)(a − b) = a² − b² to find 21 × 19.
31. 31.Find the value of x² − y² when x = 14 and y = 7.
32. 32.Find the value of x² + 2xy + y² when x = 11 and y = 1.
33. 33.Find the value of x² + 2xy + y² when x = 5 and y = 4.
34. 34.Use (a + b)(a − b) = a² − b² to find 33 × 27.
35. 35.Use (a − b)² = a² − 2ab + b² to find 86².
36. 36.Find the value of x² − 2xy + y² when x = 15 and y = 3.
37. 37.If a + b = 9 and ab = 20, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 99 × 81.
39. 39.If a + b = 20 and ab = 96, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 48².

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