Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 180 · 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 22².
2. 2.Use (a + b)² = a² + 2ab + b² to find 83².
3. 3.Use (a + b)(a − b) = a² − b² to find 48 × 32.
4. 4.If a + b = 11 and ab = 10, what is a² + b²?
5. 5.Find the value of x² − 2xy + y² when x = 5 and y = 4.
6. 6.Use (a − b)² = a² − 2ab + b² to find 28².
7. 7.Use a² − b² = (a + b)(a − b) to find 69² − 53².
8. 8.Use (a + b)(a − b) = a² − b² to find 72 × 68.
9. 9.Use (a + b)² = a² + 2ab + b² to find 43².
10. 10.Find the value of x² + 2xy + y² when x = 4 and y = 1.
11. 11.Find the value of x² + 2xy + y² when x = 13 and y = 7.
12. 12.If a + b = 13 and ab = 42, what is a² + b²?
13. 13.If a − b = 2 and ab = 15, what is a² + b²?
14. 14.Find the value of x² + 2xy + y² when x = 9 and y = 5.
15. 15.Use (a + b)(a − b) = a² − b² to find 88 × 72.
16. 16.If a − b = 2 and ab = 8, what is a² + b²?
17. 17.Find the value of x² + 2xy + y² when x = 11 and y = 8.
18. 18.If a + b = 3 and ab = 2, what is a² + b²?
19. 19.Use (a + b)(a − b) = a² − b² to find 52 × 48.
20. 20.Use (a + b)² = a² + 2ab + b² to find 52².
21. 21.Use (a − b)² = a² − 2ab + b² to find 79².
22. 22.Find the value of x² − y² when x = 11 and y = 6.
23. 23.Use (a + b)² = a² + 2ab + b² to find 33².
24. 24.Use a² − b² = (a + b)(a − b) to find 67² − 1².
25. 25.Use a² − b² = (a + b)(a − b) to find 36² − 33².
26. 26.Use a² − b² = (a + b)(a − b) to find 70² − 51².
27. 27.Use (a + b)² = a² + 2ab + b² to find 13².
28. 28.Use a² − b² = (a + b)(a − b) to find 50² − 15².
29. 29.Use (a − b)² = a² − 2ab + b² to find 82².
30. 30.Use (a − b)² = a² − 2ab + b² to find 39².
31. 31.Use (a + b)² = a² + 2ab + b² to find 97².
32. 32.Use (a + b)(a − b) = a² − b² to find 84 × 76.
33. 33.Find the value of x² − 2xy + y² when x = 13 and y = 9.
34. 34.Use (a − b)² = a² − 2ab + b² to find 72².
35. 35.Use a² − b² = (a + b)(a − b) to find 51² − 15².
36. 36.Use (a − b)² = a² − 2ab + b² to find 35².
37. 37.Use (a + b)² = a² + 2ab + b² to find 71².
38. 38.Use (a + b)² = a² + 2ab + b² to find 91².
39. 39.Use (a + b)(a − b) = a² − b² to find 67 × 53.
40. 40.Use a² − b² = (a + b)(a − b) to find 28² − 21².

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