Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 530 · 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.If a − b = 1 and ab = 12, what is a² + b²?
3. 3.Find the value of x² − 2xy + y² when x = 12 and y = 7.
4. 4.Use (a − b)² = a² − 2ab + b² to find 72².
5. 5.If a + b = 6 and ab = 8, what is a² + b²?
6. 6.Find the value of x² − y² when x = 9 and y = 3.
7. 7.Find the value of x² − 2xy + y² when x = 7 and y = 2.
8. 8.Find the value of x² + 2xy + y² when x = 6 and y = 2.
9. 9.If a − b = 4 and ab = 77, what is a² + b²?
10. 10.If a + b = 3 and ab = 2, what is a² + b²?
11. 11.Find the value of x² − y² when x = 5 and y = 1.
12. 12.Use a² − b² = (a + b)(a − b) to find 66² − 11².
13. 13.Use a² − b² = (a + b)(a − b) to find 83² − 70².
14. 14.Use (a + b)(a − b) = a² − b² to find 58 × 42.
15. 15.Use a² − b² = (a + b)(a − b) to find 75² − 4².
16. 16.Use (a + b)(a − b) = a² − b² to find 38 × 22.
17. 17.Use (a − b)² = a² − 2ab + b² to find 67².
18. 18.Use (a + b)² = a² + 2ab + b² to find 28².
19. 19.Use (a − b)² = a² − 2ab + b² to find 93².
20. 20.If a + b = 17 and ab = 72, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 74².
22. 22.Use (a − b)² = a² − 2ab + b² to find 92².
23. 23.Use (a − b)² = a² − 2ab + b² to find 79².
24. 24.Find the value of x² + 2xy + y² when x = 14 and y = 7.
25. 25.Use a² − b² = (a + b)(a − b) to find 46² − 1².
26. 26.Use a² − b² = (a + b)(a − b) to find 20² − 19².
27. 27.Use (a + b)² = a² + 2ab + b² to find 57².
28. 28.Use (a − b)² = a² − 2ab + b² to find 84².
29. 29.Use (a + b)² = a² + 2ab + b² to find 26².
30. 30.Use (a + b)² = a² + 2ab + b² to find 83².
31. 31.If a − b = 2 and ab = 8, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 11².
33. 33.If a + b = 10 and ab = 9, what is a² + b²?
34. 34.If a + b = 9 and ab = 20, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 46 × 34.
36. 36.Use (a + b)² = a² + 2ab + b² to find 84².
37. 37.Use (a + b)(a − b) = a² − b² to find 41 × 39.
38. 38.Use (a + b)(a − b) = a² − b² to find 81 × 79.
39. 39.Use (a − b)² = a² − 2ab + b² to find 15².
40. 40.Use (a + b)² = a² + 2ab + b² to find 48².

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