Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 158 · 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 + 2xy + y² when x = 7 and y = 2.
2. 2.Use a² − b² = (a + b)(a − b) to find 70² − 34².
3. 3.If a + b = 7 and ab = 10, what is a² + b²?
4. 4.If a − b = 2 and ab = 120, what is a² + b²?
5. 5.Find the value of x² − y² when x = 3 and y = 2.
6. 6.If a + b = 5 and ab = 6, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 77² − 76².
8. 8.Use (a + b)(a − b) = a² − b² to find 86 × 74.
9. 9.If a + b = 6 and ab = 5, what is a² + b²?
10. 10.Use (a + b)(a − b) = a² − b² to find 26 × 14.
11. 11.Use a² − b² = (a + b)(a − b) to find 87² − 36².
12. 12.Find the value of x² − y² when x = 14 and y = 9.
13. 13.Use (a + b)² = a² + 2ab + b² to find 19².
14. 14.Use (a + b)(a − b) = a² − b² to find 97 × 83.
15. 15.Use (a − b)² = a² − 2ab + b² to find 57².
16. 16.If a + b = 21 and ab = 108, what is a² + b²?
17. 17.Use (a + b)(a − b) = a² − b² to find 96 × 84.
18. 18.Use a² − b² = (a + b)(a − b) to find 21² − 4².
19. 19.If a − b = 3 and ab = 10, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 79² − 19².
21. 21.Use (a − b)² = a² − 2ab + b² to find 84².
22. 22.Use (a + b)(a − b) = a² − b² to find 77 × 63.
23. 23.Use (a + b)(a − b) = a² − b² to find 91 × 89.
24. 24.Use (a − b)² = a² − 2ab + b² to find 15².
25. 25.If a + b = 16 and ab = 60, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 21².
27. 27.Use (a + b)² = a² + 2ab + b² to find 57².
28. 28.If a − b = 9 and ab = 36, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 28².
30. 30.Use (a + b)² = a² + 2ab + b² to find 63².
31. 31.Find the value of x² − 2xy + y² when x = 11 and y = 10.
32. 32.Use (a + b)² = a² + 2ab + b² to find 96².
33. 33.Use (a + b)(a − b) = a² − b² to find 57 × 43.
34. 34.If a + b = 3 and ab = 2, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 53².
36. 36.Use (a + b)(a − b) = a² − b² to find 32 × 28.
37. 37.If a + b = 4 and ab = 3, what is a² + b²?
38. 38.Find the value of x² − y² when x = 11 and y = 3.
39. 39.Use a² − b² = (a + b)(a − b) to find 69² − 24².
40. 40.Use (a − b)² = a² − 2ab + b² to find 66².

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