Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 148 · 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.Use (a − b)² = a² − 2ab + b² to find 99².
3. 3.Use a² − b² = (a + b)(a − b) to find 60² − 41².
4. 4.Use a² − b² = (a + b)(a − b) to find 21² − 1².
5. 5.If a + b = 7 and ab = 12, what is a² + b²?
6. 6.Find the value of x² + 2xy + y² when x = 5 and y = 3.
7. 7.Use (a − b)² = a² − 2ab + b² to find 89².
8. 8.Find the value of x² − y² when x = 6 and y = 3.
9. 9.Find the value of x² + 2xy + y² when x = 13 and y = 5.
10. 10.Use a² − b² = (a + b)(a − b) to find 27² − 6².
11. 11.Use (a + b)(a − b) = a² − b² to find 67 × 53.
12. 12.Use (a + b)(a − b) = a² − b² to find 35 × 25.
13. 13.Use (a + b)² = a² + 2ab + b² to find 41².
14. 14.Use (a + b)(a − b) = a² − b² to find 98 × 82.
15. 15.Use (a − b)² = a² − 2ab + b² to find 76².
16. 16.Use a² − b² = (a + b)(a − b) to find 57² − 31².
17. 17.Use (a + b)(a − b) = a² − b² to find 25 × 15.
18. 18.Use a² − b² = (a + b)(a − b) to find 86² − 6².
19. 19.If a − b = 1 and ab = 12, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 41 × 39.
21. 21.If a − b = 5 and ab = 6, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 68².
23. 23.Use (a − b)² = a² − 2ab + b² to find 37².
24. 24.Use (a + b)(a − b) = a² − b² to find 32 × 28.
25. 25.Use (a + b)(a − b) = a² − b² to find 55 × 45.
26. 26.If a + b = 14 and ab = 45, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 16².
28. 28.Use (a + b)² = a² + 2ab + b² to find 49².
29. 29.Use (a + b)(a − b) = a² − b² to find 49 × 31.
30. 30.Find the value of x² + 2xy + y² when x = 3 and y = 2.
31. 31.Find the value of x² + 2xy + y² when x = 12 and y = 8.
32. 32.Use (a − b)² = a² − 2ab + b² to find 73².
33. 33.Use a² − b² = (a + b)(a − b) to find 87² − 13².
34. 34.Find the value of x² − y² when x = 3 and y = 2.
35. 35.Use a² − b² = (a + b)(a − b) to find 81² − 47².
36. 36.Use (a − b)² = a² − 2ab + b² to find 62².
37. 37.Use (a − b)² = a² − 2ab + b² to find 87².
38. 38.Use (a + b)(a − b) = a² − b² to find 26 × 14.
39. 39.Use (a + b)² = a² + 2ab + b² to find 28².
40. 40.If a + b = 21 and ab = 110, what is a² + b²?

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