Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 217 · 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 a² − b² = (a + b)(a − b) to find 41² − 28².
2. 2.Use (a + b)(a − b) = a² − b² to find 79 × 61.
3. 3.Find the value of x² + 2xy + y² when x = 6 and y = 4.
4. 4.Find the value of x² − 2xy + y² when x = 15 and y = 12.
5. 5.Use (a + b)² = a² + 2ab + b² to find 14².
6. 6.If a + b = 5 and ab = 6, what is a² + b²?
7. 7.If a − b = 1 and ab = 30, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 32².
9. 9.Use (a + b)² = a² + 2ab + b² to find 83².
10. 10.Use a² − b² = (a + b)(a − b) to find 32² − 14².
11. 11.Use (a − b)² = a² − 2ab + b² to find 14².
12. 12.Use (a + b)(a − b) = a² − b² to find 87 × 73.
13. 13.If a − b = 1 and ab = 72, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 21².
15. 15.Use (a + b)(a − b) = a² − b² to find 38 × 22.
16. 16.Use (a − b)² = a² − 2ab + b² to find 96².
17. 17.Use (a + b)(a − b) = a² − b² to find 103 × 97.
18. 18.Use a² − b² = (a + b)(a − b) to find 31² − 25².
19. 19.Use (a − b)² = a² − 2ab + b² to find 12².
20. 20.Use (a − b)² = a² − 2ab + b² to find 75².
21. 21.Find the value of x² − y² when x = 4 and y = 2.
22. 22.Use (a − b)² = a² − 2ab + b² to find 48².
23. 23.Use (a + b)² = a² + 2ab + b² to find 69².
24. 24.Use (a − b)² = a² − 2ab + b² to find 28².
25. 25.Use (a + b)(a − b) = a² − b² to find 22 × 18.
26. 26.Use (a + b)(a − b) = a² − b² to find 104 × 96.
27. 27.Use a² − b² = (a + b)(a − b) to find 77² − 24².
28. 28.If a + b = 7 and ab = 10, what is a² + b²?
29. 29.Find the value of x² − 2xy + y² when x = 12 and y = 7.
30. 30.Use a² − b² = (a + b)(a − b) to find 76² − 55².
31. 31.Use a² − b² = (a + b)(a − b) to find 21² − 11².
32. 32.Find the value of x² − 2xy + y² when x = 12 and y = 9.
33. 33.Use (a + b)² = a² + 2ab + b² to find 95².
34. 34.Use a² − b² = (a + b)(a − b) to find 24² − 8².
35. 35.Use (a − b)² = a² − 2ab + b² to find 11².
36. 36.Find the value of x² − 2xy + y² when x = 3 and y = 1.
37. 37.Use a² − b² = (a + b)(a − b) to find 69² − 57².
38. 38.Use (a + b)(a − b) = a² − b² to find 54 × 46.
39. 39.Use a² − b² = (a + b)(a − b) to find 27² − 3².
40. 40.Find the value of x² − y² when x = 8 and y = 5.

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