Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 863 · 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 93².
2. 2.Find the value of x² + 2xy + y² when x = 14 and y = 8.
3. 3.Use (a − b)² = a² − 2ab + b² to find 38².
4. 4.If a − b = 5 and ab = 6, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 67 × 53.
6. 6.If a − b = 2 and ab = 8, what is a² + b²?
7. 7.Use (a + b)(a − b) = a² − b² to find 81 × 79.
8. 8.If a + b = 8 and ab = 7, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 86².
10. 10.Find the value of x² + 2xy + y² when x = 14 and y = 6.
11. 11.Use (a + b)(a − b) = a² − b² to find 77 × 63.
12. 12.Use (a + b)(a − b) = a² − b² to find 22 × 18.
13. 13.If a − b = 6 and ab = 72, what is a² + b²?
14. 14.Find the value of x² − y² when x = 5 and y = 3.
15. 15.Find the value of x² − 2xy + y² when x = 11 and y = 8.
16. 16.Use (a + b)(a − b) = a² − b² to find 74 × 66.
17. 17.Use (a + b)² = a² + 2ab + b² to find 99².
18. 18.Use a² − b² = (a + b)(a − b) to find 98² − 20².
19. 19.Use (a + b)² = a² + 2ab + b² to find 42².
20. 20.Use a² − b² = (a + b)(a − b) to find 66² − 19².
21. 21.If a + b = 15 and ab = 56, what is a² + b²?
22. 22.If a + b = 13 and ab = 40, what is a² + b²?
23. 23.Find the value of x² + 2xy + y² when x = 9 and y = 1.
24. 24.Use (a + b)(a − b) = a² − b² to find 56 × 44.
25. 25.Find the value of x² + 2xy + y² when x = 12 and y = 4.
26. 26.Find the value of x² − 2xy + y² when x = 15 and y = 9.
27. 27.Find the value of x² − y² when x = 5 and y = 1.
28. 28.Find the value of x² + 2xy + y² when x = 3 and y = 2.
29. 29.Use a² − b² = (a + b)(a − b) to find 73² − 41².
30. 30.Use (a + b)(a − b) = a² − b² to find 39 × 21.
31. 31.Use (a − b)² = a² − 2ab + b² to find 94².
32. 32.Use a² − b² = (a + b)(a − b) to find 87² − 41².
33. 33.Use (a + b)² = a² + 2ab + b² to find 17².
34. 34.Find the value of x² − 2xy + y² when x = 12 and y = 10.
35. 35.Use (a − b)² = a² − 2ab + b² to find 61².
36. 36.Use a² − b² = (a + b)(a − b) to find 74² − 63².
37. 37.If a + b = 5 and ab = 6, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 76².
39. 39.Use (a + b)(a − b) = a² − b² to find 86 × 74.
40. 40.Use (a − b)² = a² − 2ab + b² to find 19².

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