Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 209 · 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 a² − b² = (a + b)(a − b) to find 69² − 47².
2. 2.Use (a + b)² = a² + 2ab + b² to find 83².
3. 3.If a − b = 8 and ab = 9, what is a² + b²?
4. 4.Use (a + b)(a − b) = a² − b² to find 49 × 31.
5. 5.Use (a + b)² = a² + 2ab + b² to find 13².
6. 6.Use (a + b)(a − b) = a² − b² to find 43 × 37.
7. 7.Use (a + b)² = a² + 2ab + b² to find 71².
8. 8.Use (a + b)² = a² + 2ab + b² to find 33².
9. 9.Use (a + b)(a − b) = a² − b² to find 39 × 21.
10. 10.If a + b = 3 and ab = 2, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 85 × 75.
12. 12.Use (a − b)² = a² − 2ab + b² to find 87².
13. 13.Use a² − b² = (a + b)(a − b) to find 61² − 59².
14. 14.Use (a + b)(a − b) = a² − b² to find 23 × 17.
15. 15.Use a² − b² = (a + b)(a − b) to find 83² − 11².
16. 16.If a − b = 3 and ab = 18, what is a² + b²?
17. 17.If a + b = 20 and ab = 99, what is a² + b²?
18. 18.Use (a + b)² = a² + 2ab + b² to find 61².
19. 19.Use a² − b² = (a + b)(a − b) to find 20² − 6².
20. 20.Use (a + b)(a − b) = a² − b² to find 48 × 32.
21. 21.Use (a + b)² = a² + 2ab + b² to find 54².
22. 22.Use a² − b² = (a + b)(a − b) to find 23² − 4².
23. 23.Use (a − b)² = a² − 2ab + b² to find 79².
24. 24.Use (a + b)(a − b) = a² − b² to find 65 × 55.
25. 25.Use (a + b)² = a² + 2ab + b² to find 14².
26. 26.Use (a + b)(a − b) = a² − b² to find 31 × 29.
27. 27.Use a² − b² = (a + b)(a − b) to find 74² − 16².
28. 28.If a − b = 1 and ab = 12, what is a² + b²?
29. 29.If a + b = 15 and ab = 56, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 36².
31. 31.Use (a − b)² = a² − 2ab + b² to find 96².
32. 32.Use (a + b)² = a² + 2ab + b² to find 34².
33. 33.Use (a − b)² = a² − 2ab + b² to find 37².
34. 34.Use (a + b)² = a² + 2ab + b² to find 87².
35. 35.Use (a + b)² = a² + 2ab + b² to find 75².
36. 36.Find the value of x² + 2xy + y² when x = 3 and y = 2.
37. 37.Find the value of x² − 2xy + y² when x = 11 and y = 10.
38. 38.Use (a + b)(a − b) = a² − b² to find 47 × 33.
39. 39.Find the value of x² − 2xy + y² when x = 14 and y = 5.
40. 40.Use (a + b)² = a² + 2ab + b² to find 58².

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