Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 699 · 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 (a + b)(a − b) = a² − b² to find 103 × 97.
2. 2.Use (a − b)² = a² − 2ab + b² to find 19².
3. 3.Find the value of x² − 2xy + y² when x = 8 and y = 2.
4. 4.Use (a + b)² = a² + 2ab + b² to find 61².
5. 5.Find the value of x² − 2xy + y² when x = 10 and y = 3.
6. 6.Use a² − b² = (a + b)(a − b) to find 78² − 16².
7. 7.Find the value of x² − y² when x = 11 and y = 1.
8. 8.Find the value of x² + 2xy + y² when x = 8 and y = 1.
9. 9.Use (a + b)² = a² + 2ab + b² to find 21².
10. 10.If a − b = 3 and ab = 10, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 12².
12. 12.Use (a + b)² = a² + 2ab + b² to find 26².
13. 13.Use (a + b)² = a² + 2ab + b² to find 22².
14. 14.Find the value of x² − 2xy + y² when x = 12 and y = 6.
15. 15.Use (a + b)² = a² + 2ab + b² to find 81².
16. 16.Use a² − b² = (a + b)(a − b) to find 73² − 30².
17. 17.Use (a + b)(a − b) = a² − b² to find 107 × 93.
18. 18.Find the value of x² − y² when x = 8 and y = 2.
19. 19.Use (a − b)² = a² − 2ab + b² to find 55².
20. 20.Use a² − b² = (a + b)(a − b) to find 52² − 5².
21. 21.Use (a + b)(a − b) = a² − b² to find 57 × 43.
22. 22.Use a² − b² = (a + b)(a − b) to find 64² − 49².
23. 23.Use (a + b)² = a² + 2ab + b² to find 42².
24. 24.If a − b = 4 and ab = 96, what is a² + b²?
25. 25.Find the value of x² + 2xy + y² when x = 7 and y = 2.
26. 26.Find the value of x² + 2xy + y² when x = 4 and y = 2.
27. 27.Find the value of x² + 2xy + y² when x = 7 and y = 4.
28. 28.Use a² − b² = (a + b)(a − b) to find 37² − 3².
29. 29.Use a² − b² = (a + b)(a − b) to find 30² − 15².
30. 30.Use (a − b)² = a² − 2ab + b² to find 34².
31. 31.Use (a + b)(a − b) = a² − b² to find 34 × 26.
32. 32.Use (a + b)² = a² + 2ab + b² to find 45².
33. 33.Use a² − b² = (a + b)(a − b) to find 70² − 63².
34. 34.Use (a + b)² = a² + 2ab + b² to find 38².
35. 35.Use (a + b)² = a² + 2ab + b² to find 24².
36. 36.Use (a − b)² = a² − 2ab + b² to find 42².
37. 37.Use (a + b)(a − b) = a² − b² to find 46 × 34.
38. 38.Use (a + b)(a − b) = a² − b² to find 84 × 76.
39. 39.Find the value of x² − 2xy + y² when x = 6 and y = 4.
40. 40.Use (a + b)(a − b) = a² − b² to find 35 × 25.

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