Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 169 · 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.Find the value of x² − y² when x = 7 and y = 3.
2. 2.Find the value of x² − 2xy + y² when x = 4 and y = 3.
3. 3.Use (a + b)² = a² + 2ab + b² to find 85².
4. 4.Use (a − b)² = a² − 2ab + b² to find 96².
5. 5.Use (a + b)² = a² + 2ab + b² to find 66².
6. 6.If a + b = 6 and ab = 8, what is a² + b²?
7. 7.If a + b = 9 and ab = 18, what is a² + b²?
8. 8.Find the value of x² − 2xy + y² when x = 3 and y = 1.
9. 9.Find the value of x² − 2xy + y² when x = 14 and y = 13.
10. 10.Use (a + b)² = a² + 2ab + b² to find 82².
11. 11.Use a² − b² = (a + b)(a − b) to find 47² − 29².
12. 12.Use (a − b)² = a² − 2ab + b² to find 93².
13. 13.Use (a + b)² = a² + 2ab + b² to find 35².
14. 14.Use (a − b)² = a² − 2ab + b² to find 65².
15. 15.Use (a + b)² = a² + 2ab + b² to find 69².
16. 16.If a + b = 5 and ab = 6, what is a² + b²?
17. 17.Find the value of x² + 2xy + y² when x = 5 and y = 2.
18. 18.Use a² − b² = (a + b)(a − b) to find 41² − 15².
19. 19.Use (a − b)² = a² − 2ab + b² to find 62².
20. 20.Find the value of x² + 2xy + y² when x = 14 and y = 9.
21. 21.If a − b = 1 and ab = 2, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 17².
23. 23.Use a² − b² = (a + b)(a − b) to find 69² − 24².
24. 24.Use (a + b)² = a² + 2ab + b² to find 68².
25. 25.Use a² − b² = (a + b)(a − b) to find 44² − 3².
26. 26.If a + b = 4 and ab = 3, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 45 × 35.
28. 28.Use (a + b)² = a² + 2ab + b² to find 15².
29. 29.Find the value of x² + 2xy + y² when x = 9 and y = 4.
30. 30.Use (a + b)² = a² + 2ab + b² to find 52².
31. 31.Use (a + b)(a − b) = a² − b² to find 91 × 89.
32. 32.If a + b = 8 and ab = 15, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 72².
34. 34.If a + b = 15 and ab = 56, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 36².
36. 36.Use (a + b)(a − b) = a² − b² to find 84 × 76.
37. 37.If a + b = 3 and ab = 2, what is a² + b²?
38. 38.Find the value of x² − y² when x = 13 and y = 7.
39. 39.Use a² − b² = (a + b)(a − b) to find 82² − 15².
40. 40.Use a² − b² = (a + b)(a − b) to find 52² − 26².

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