Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 14 · 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 38².
2. 2.Use (a − b)² = a² − 2ab + b² to find 35².
3. 3.If a − b = 1 and ab = 2, what is a² + b²?
4. 4.If a + b = 5 and ab = 6, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 69² − 63².
6. 6.Use (a − b)² = a² − 2ab + b² to find 15².
7. 7.Find the value of x² − y² when x = 5 and y = 2.
8. 8.Find the value of x² − y² when x = 11 and y = 1.
9. 9.Find the value of x² − y² when x = 8 and y = 3.
10. 10.Find the value of x² − 2xy + y² when x = 5 and y = 3.
11. 11.Use a² − b² = (a + b)(a − b) to find 62² − 47².
12. 12.Use a² − b² = (a + b)(a − b) to find 94² − 27².
13. 13.Use (a + b)² = a² + 2ab + b² to find 13².
14. 14.Use (a + b)² = a² + 2ab + b² to find 42².
15. 15.Find the value of x² − y² when x = 10 and y = 1.
16. 16.Find the value of x² − 2xy + y² when x = 11 and y = 8.
17. 17.Use (a + b)(a − b) = a² − b² to find 45 × 35.
18. 18.If a + b = 11 and ab = 24, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 37² − 32².
20. 20.Use (a + b)² = a² + 2ab + b² to find 46².
21. 21.Use (a − b)² = a² − 2ab + b² to find 32².
22. 22.Use (a + b)² = a² + 2ab + b² to find 71².
23. 23.Use (a + b)² = a² + 2ab + b² to find 93².
24. 24.If a + b = 9 and ab = 20, what is a² + b²?
25. 25.Find the value of x² − 2xy + y² when x = 6 and y = 5.
26. 26.Use (a + b)(a − b) = a² − b² to find 23 × 17.
27. 27.Find the value of x² − 2xy + y² when x = 15 and y = 2.
28. 28.Use (a + b)(a − b) = a² − b² to find 68 × 52.
29. 29.If a + b = 15 and ab = 44, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 52².
31. 31.Find the value of x² + 2xy + y² when x = 11 and y = 1.
32. 32.Use (a + b)(a − b) = a² − b² to find 79 × 61.
33. 33.Use (a + b)(a − b) = a² − b² to find 36 × 24.
34. 34.Use (a + b)(a − b) = a² − b² to find 38 × 22.
35. 35.Use (a + b)² = a² + 2ab + b² to find 102².
36. 36.Use a² − b² = (a + b)(a − b) to find 33² − 12².
37. 37.Use (a + b)(a − b) = a² − b² to find 26 × 14.
38. 38.Use (a − b)² = a² − 2ab + b² to find 14².
39. 39.Use a² − b² = (a + b)(a − b) to find 42² − 23².
40. 40.Use (a + b)(a − b) = a² − b² to find 99 × 81.

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