Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 224 · 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)² = a² + 2ab + b² to find 97².
2. 2.Find the value of x² − 2xy + y² when x = 5 and y = 2.
3. 3.Use (a − b)² = a² − 2ab + b² to find 19².
4. 4.Use (a − b)² = a² − 2ab + b² to find 42².
5. 5.If a + b = 5 and ab = 4, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 80² − 56².
7. 7.Use (a − b)² = a² − 2ab + b² to find 67².
8. 8.Use a² − b² = (a + b)(a − b) to find 36² − 22².
9. 9.Use (a − b)² = a² − 2ab + b² to find 55².
10. 10.Find the value of x² − 2xy + y² when x = 7 and y = 4.
11. 11.Use (a − b)² = a² − 2ab + b² to find 38².
12. 12.Find the value of x² − 2xy + y² when x = 7 and y = 1.
13. 13.Use (a + b)² = a² + 2ab + b² to find 54².
14. 14.Use (a − b)² = a² − 2ab + b² to find 26².
15. 15.Use (a + b)(a − b) = a² − b² to find 72 × 68.
16. 16.Use (a + b)² = a² + 2ab + b² to find 109².
17. 17.Use (a − b)² = a² − 2ab + b² to find 32².
18. 18.Use (a + b)² = a² + 2ab + b² to find 78².
19. 19.Find the value of x² − 2xy + y² when x = 8 and y = 4.
20. 20.Use a² − b² = (a + b)(a − b) to find 27² − 14².
21. 21.Find the value of x² + 2xy + y² when x = 10 and y = 5.
22. 22.Find the value of x² + 2xy + y² when x = 3 and y = 2.
23. 23.Use (a + b)(a − b) = a² − b² to find 84 × 76.
24. 24.Find the value of x² − 2xy + y² when x = 9 and y = 4.
25. 25.Use a² − b² = (a + b)(a − b) to find 71² − 60².
26. 26.Find the value of x² − 2xy + y² when x = 10 and y = 4.
27. 27.Find the value of x² + 2xy + y² when x = 5 and y = 3.
28. 28.Use (a + b)(a − b) = a² − b² to find 71 × 69.
29. 29.Use (a − b)² = a² − 2ab + b² to find 73².
30. 30.Use (a + b)² = a² + 2ab + b² to find 95².
31. 31.Use (a + b)² = a² + 2ab + b² to find 41².
32. 32.Use (a − b)² = a² − 2ab + b² to find 79².
33. 33.If a − b = 4 and ab = 77, what is a² + b²?
34. 34.Find the value of x² + 2xy + y² when x = 14 and y = 8.
35. 35.Use (a + b)² = a² + 2ab + b² to find 91².
36. 36.Use (a − b)² = a² − 2ab + b² to find 81².
37. 37.Use (a − b)² = a² − 2ab + b² to find 63².
38. 38.Use (a + b)² = a² + 2ab + b² to find 18².
39. 39.Use (a − b)² = a² − 2ab + b² to find 16².
40. 40.If a − b = 1 and ab = 2, what is a² + b²?

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