Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 877 · 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 19².
2. 2.If a + b = 3 and ab = 2, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 39².
4. 4.Find the value of x² + 2xy + y² when x = 11 and y = 3.
5. 5.Use a² − b² = (a + b)(a − b) to find 80² − 9².
6. 6.Use a² − b² = (a + b)(a − b) to find 91² − 30².
7. 7.Use (a + b)² = a² + 2ab + b² to find 58².
8. 8.Use (a − b)² = a² − 2ab + b² to find 46².
9. 9.Use (a + b)(a − b) = a² − b² to find 57 × 43.
10. 10.If a + b = 8 and ab = 12, what is a² + b²?
11. 11.Find the value of x² + 2xy + y² when x = 14 and y = 1.
12. 12.Use (a + b)(a − b) = a² − b² to find 89 × 71.
13. 13.Find the value of x² + 2xy + y² when x = 15 and y = 14.
14. 14.Use (a + b)² = a² + 2ab + b² to find 31².
15. 15.Find the value of x² − 2xy + y² when x = 7 and y = 3.
16. 16.Use (a + b)² = a² + 2ab + b² to find 17².
17. 17.Use a² − b² = (a + b)(a − b) to find 49² − 25².
18. 18.Use (a + b)(a − b) = a² − b² to find 43 × 37.
19. 19.Use (a + b)² = a² + 2ab + b² to find 81².
20. 20.Use (a + b)(a − b) = a² − b² to find 102 × 98.
21. 21.Use (a − b)² = a² − 2ab + b² to find 42².
22. 22.Use (a − b)² = a² − 2ab + b² to find 14².
23. 23.Use (a + b)(a − b) = a² − b² to find 22 × 18.
24. 24.Use (a + b)² = a² + 2ab + b² to find 16².
25. 25.Use a² − b² = (a + b)(a − b) to find 57² − 42².
26. 26.Use (a + b)² = a² + 2ab + b² to find 41².
27. 27.Find the value of x² − 2xy + y² when x = 4 and y = 3.
28. 28.Use a² − b² = (a + b)(a − b) to find 37² − 6².
29. 29.Use (a + b)(a − b) = a² − b² to find 32 × 28.
30. 30.Use (a − b)² = a² − 2ab + b² to find 15².
31. 31.Use a² − b² = (a + b)(a − b) to find 39² − 35².
32. 32.Use (a + b)(a − b) = a² − b² to find 45 × 35.
33. 33.Find the value of x² + 2xy + y² when x = 13 and y = 9.
34. 34.Find the value of x² − 2xy + y² when x = 11 and y = 3.
35. 35.If a + b = 7 and ab = 6, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 59².
37. 37.Use (a + b)(a − b) = a² − b² to find 35 × 25.
38. 38.Use (a − b)² = a² − 2ab + b² to find 69².
39. 39.Use (a + b)² = a² + 2ab + b² to find 65².
40. 40.Find the value of x² + 2xy + y² when x = 9 and y = 7.

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