Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 686 · 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 = 3 and y = 2.
2. 2.If a + b = 7 and ab = 6, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 94².
4. 4.Use (a − b)² = a² − 2ab + b² to find 34².
5. 5.Use (a − b)² = a² − 2ab + b² to find 22².
6. 6.Use (a + b)(a − b) = a² − b² to find 26 × 14.
7. 7.Use (a − b)² = a² − 2ab + b² to find 87².
8. 8.Use a² − b² = (a + b)(a − b) to find 77² − 1².
9. 9.If a − b = 1 and ab = 2, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 65².
11. 11.If a + b = 13 and ab = 30, what is a² + b²?
12. 12.Use (a − b)² = a² − 2ab + b² to find 15².
13. 13.Use (a + b)² = a² + 2ab + b² to find 36².
14. 14.Use (a + b)² = a² + 2ab + b² to find 19².
15. 15.Find the value of x² + 2xy + y² when x = 8 and y = 5.
16. 16.Use (a − b)² = a² − 2ab + b² to find 61².
17. 17.Find the value of x² + 2xy + y² when x = 8 and y = 3.
18. 18.If a − b = 4 and ab = 21, what is a² + b²?
19. 19.If a − b = 9 and ab = 22, what is a² + b²?
20. 20.If a − b = 11 and ab = 12, what is a² + b²?
21. 21.Find the value of x² + 2xy + y² when x = 9 and y = 7.
22. 22.Use (a + b)² = a² + 2ab + b² to find 88².
23. 23.Use (a + b)(a − b) = a² − b² to find 27 × 13.
24. 24.Use (a + b)² = a² + 2ab + b² to find 35².
25. 25.Use a² − b² = (a + b)(a − b) to find 82² − 18².
26. 26.Use (a − b)² = a² − 2ab + b² to find 48².
27. 27.If a + b = 12 and ab = 20, what is a² + b²?
28. 28.If a − b = 5 and ab = 50, what is a² + b²?
29. 29.If a − b = 4 and ab = 96, what is a² + b²?
30. 30.Find the value of x² − y² when x = 9 and y = 7.
31. 31.If a + b = 7 and ab = 12, what is a² + b²?
32. 32.Find the value of x² − y² when x = 7 and y = 3.
33. 33.Use (a + b)² = a² + 2ab + b² to find 51².
34. 34.Use a² − b² = (a + b)(a − b) to find 36² − 21².
35. 35.Use (a + b)(a − b) = a² − b² to find 95 × 85.
36. 36.Find the value of x² + 2xy + y² when x = 3 and y = 1.
37. 37.Use (a + b)² = a² + 2ab + b² to find 49².
38. 38.Find the value of x² + 2xy + y² when x = 3 and y = 2.
39. 39.Use (a + b)(a − b) = a² − b² to find 55 × 45.
40. 40.Use (a − b)² = a² − 2ab + b² to find 85².

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