Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 373 · 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 = 4 and y = 3.
2. 2.Use a² − b² = (a + b)(a − b) to find 90² − 29².
3. 3.Use (a − b)² = a² − 2ab + b² to find 61².
4. 4.Use (a + b)² = a² + 2ab + b² to find 18².
5. 5.Use (a + b)² = a² + 2ab + b² to find 77².
6. 6.Use (a + b)² = a² + 2ab + b² to find 11².
7. 7.Use a² − b² = (a + b)(a − b) to find 59² − 49².
8. 8.If a − b = 3 and ab = 70, what is a² + b²?
9. 9.If a − b = 4 and ab = 12, what is a² + b²?
10. 10.Find the value of x² + 2xy + y² when x = 11 and y = 8.
11. 11.Use (a − b)² = a² − 2ab + b² to find 73².
12. 12.Use a² − b² = (a + b)(a − b) to find 98² − 59².
13. 13.Use (a − b)² = a² − 2ab + b² to find 16².
14. 14.Find the value of x² + 2xy + y² when x = 15 and y = 11.
15. 15.If a + b = 3 and ab = 2, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 44².
17. 17.Use a² − b² = (a + b)(a − b) to find 23² − 12².
18. 18.Use (a + b)(a − b) = a² − b² to find 47 × 33.
19. 19.Use (a − b)² = a² − 2ab + b² to find 88².
20. 20.Use (a + b)² = a² + 2ab + b² to find 49².
21. 21.Use (a + b)² = a² + 2ab + b² to find 12².
22. 22.Use (a − b)² = a² − 2ab + b² to find 29².
23. 23.Use (a + b)² = a² + 2ab + b² to find 16².
24. 24.Use a² − b² = (a + b)(a − b) to find 74² − 62².
25. 25.Use (a − b)² = a² − 2ab + b² to find 45².
26. 26.Use (a + b)(a − b) = a² − b² to find 105 × 95.
27. 27.Find the value of x² + 2xy + y² when x = 3 and y = 2.
28. 28.Use (a + b)² = a² + 2ab + b² to find 22².
29. 29.Use (a + b)² = a² + 2ab + b² to find 74².
30. 30.Use (a + b)(a − b) = a² − b² to find 55 × 45.
31. 31.Use (a + b)² = a² + 2ab + b² to find 43².
32. 32.Use (a + b)² = a² + 2ab + b² to find 53².
33. 33.Use (a + b)(a − b) = a² − b² to find 73 × 67.
34. 34.Use (a + b)(a − b) = a² − b² to find 65 × 55.
35. 35.Use (a + b)² = a² + 2ab + b² to find 63².
36. 36.Use a² − b² = (a + b)(a − b) to find 66² − 9².
37. 37.Find the value of x² − y² when x = 5 and y = 3.
38. 38.Use (a + b)² = a² + 2ab + b² to find 108².
39. 39.If a + b = 15 and ab = 44, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 45 × 35.

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