Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 935 · 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 27².
2. 2.If a − b = 3 and ab = 4, what is a² + b²?
3. 3.Find the value of x² − y² when x = 14 and y = 11.
4. 4.Use (a − b)² = a² − 2ab + b² to find 17².
5. 5.Find the value of x² − y² when x = 7 and y = 6.
6. 6.Use (a − b)² = a² − 2ab + b² to find 37².
7. 7.Use (a + b)(a − b) = a² − b² to find 22 × 18.
8. 8.Use (a + b)(a − b) = a² − b² to find 23 × 17.
9. 9.Find the value of x² − y² when x = 13 and y = 9.
10. 10.Use (a − b)² = a² − 2ab + b² to find 73².
11. 11.Use (a + b)(a − b) = a² − b² to find 72 × 68.
12. 12.If a − b = 9 and ab = 22, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 12².
14. 14.Use a² − b² = (a + b)(a − b) to find 87² − 28².
15. 15.If a + b = 13 and ab = 42, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 59².
17. 17.Use a² − b² = (a + b)(a − b) to find 42² − 33².
18. 18.Use a² − b² = (a + b)(a − b) to find 62² − 29².
19. 19.Use (a + b)² = a² + 2ab + b² to find 37².
20. 20.Use (a − b)² = a² − 2ab + b² to find 23².
21. 21.Use a² − b² = (a + b)(a − b) to find 84² − 83².
22. 22.Use a² − b² = (a + b)(a − b) to find 95² − 70².
23. 23.Use a² − b² = (a + b)(a − b) to find 69² − 42².
24. 24.Use (a + b)(a − b) = a² − b² to find 36 × 24.
25. 25.Use (a + b)² = a² + 2ab + b² to find 32².
26. 26.Use (a − b)² = a² − 2ab + b² to find 55².
27. 27.If a + b = 17 and ab = 72, what is a² + b²?
28. 28.Find the value of x² + 2xy + y² when x = 6 and y = 1.
29. 29.If a + b = 10 and ab = 21, what is a² + b²?
30. 30.If a + b = 21 and ab = 108, what is a² + b²?
31. 31.Use (a − b)² = a² − 2ab + b² to find 45².
32. 32.Use (a + b)(a − b) = a² − b² to find 47 × 33.
33. 33.Use a² − b² = (a + b)(a − b) to find 63² − 29².
34. 34.Use a² − b² = (a + b)(a − b) to find 89² − 1².
35. 35.Use a² − b² = (a + b)(a − b) to find 69² − 26².
36. 36.Find the value of x² − 2xy + y² when x = 11 and y = 6.
37. 37.Use a² − b² = (a + b)(a − b) to find 27² − 2².
38. 38.If a − b = 3 and ab = 10, what is a² + b²?
39. 39.Find the value of x² + 2xy + y² when x = 11 and y = 2.
40. 40.Use (a − b)² = a² − 2ab + b² to find 22².

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