Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 88 · 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 15².
2. 2.If a + b = 17 and ab = 72, what is a² + b²?
3. 3.If a − b = 1 and ab = 6, what is a² + b²?
4. 4.Find the value of x² + 2xy + y² when x = 12 and y = 11.
5. 5.Find the value of x² − y² when x = 6 and y = 3.
6. 6.Use a² − b² = (a + b)(a − b) to find 93² − 5².
7. 7.Find the value of x² − 2xy + y² when x = 12 and y = 8.
8. 8.Use (a − b)² = a² − 2ab + b² to find 85².
9. 9.Use (a − b)² = a² − 2ab + b² to find 75².
10. 10.Use (a + b)² = a² + 2ab + b² to find 107².
11. 11.Use a² − b² = (a + b)(a − b) to find 38² − 8².
12. 12.Find the value of x² − y² when x = 3 and y = 1.
13. 13.Use (a − b)² = a² − 2ab + b² to find 46².
14. 14.Use a² − b² = (a + b)(a − b) to find 60² − 21².
15. 15.Use a² − b² = (a + b)(a − b) to find 97² − 27².
16. 16.Use (a + b)(a − b) = a² − b² to find 24 × 16.
17. 17.Use (a + b)(a − b) = a² − b² to find 105 × 95.
18. 18.Find the value of x² − y² when x = 8 and y = 1.
19. 19.Use (a + b)(a − b) = a² − b² to find 98 × 82.
20. 20.Use a² − b² = (a + b)(a − b) to find 31² − 29².
21. 21.Find the value of x² − 2xy + y² when x = 8 and y = 1.
22. 22.If a + b = 6 and ab = 8, what is a² + b²?
23. 23.Use (a + b)² = a² + 2ab + b² to find 51².
24. 24.Use (a + b)² = a² + 2ab + b² to find 36².
25. 25.Use (a − b)² = a² − 2ab + b² to find 74².
26. 26.Use (a − b)² = a² − 2ab + b² to find 94².
27. 27.Use (a + b)² = a² + 2ab + b² to find 73².
28. 28.Use (a − b)² = a² − 2ab + b² to find 16².
29. 29.Use (a + b)(a − b) = a² − b² to find 43 × 37.
30. 30.Use (a + b)(a − b) = a² − b² to find 34 × 26.
31. 31.Use (a + b)² = a² + 2ab + b² to find 62².
32. 32.Find the value of x² + 2xy + y² when x = 8 and y = 2.
33. 33.Find the value of x² − 2xy + y² when x = 9 and y = 2.
34. 34.Find the value of x² − y² when x = 9 and y = 8.
35. 35.Use (a − b)² = a² − 2ab + b² to find 64².
36. 36.Use (a + b)(a − b) = a² − b² to find 94 × 86.
37. 37.If a + b = 9 and ab = 8, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 57².
39. 39.Use (a − b)² = a² − 2ab + b² to find 33².
40. 40.Use (a + b)² = a² + 2ab + b² to find 34².

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