Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 451 · 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.Find the value of x² + 2xy + y² when x = 12 and y = 10.
2. 2.Use (a − b)² = a² − 2ab + b² to find 46².
3. 3.Use (a + b)(a − b) = a² − b² to find 84 × 76.
4. 4.Use (a + b)(a − b) = a² − b² to find 73 × 67.
5. 5.Use (a + b)(a − b) = a² − b² to find 76 × 64.
6. 6.Use (a + b)² = a² + 2ab + b² to find 94².
7. 7.If a + b = 20 and ab = 99, what is a² + b²?
8. 8.Find the value of x² − 2xy + y² when x = 6 and y = 5.
9. 9.Find the value of x² − 2xy + y² when x = 8 and y = 1.
10. 10.Use (a − b)² = a² − 2ab + b² to find 28².
11. 11.Use (a + b)² = a² + 2ab + b² to find 107².
12. 12.Use (a − b)² = a² − 2ab + b² to find 49².
13. 13.Use (a − b)² = a² − 2ab + b² to find 24².
14. 14.Use (a + b)² = a² + 2ab + b² to find 55².
15. 15.Use (a + b)² = a² + 2ab + b² to find 27².
16. 16.If a + b = 5 and ab = 4, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 32².
18. 18.Use (a − b)² = a² − 2ab + b² to find 27².
19. 19.Use (a + b)² = a² + 2ab + b² to find 16².
20. 20.If a + b = 7 and ab = 10, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 95 × 85.
22. 22.Use (a − b)² = a² − 2ab + b² to find 37².
23. 23.Use (a + b)² = a² + 2ab + b² to find 105².
24. 24.Use (a + b)² = a² + 2ab + b² to find 97².
25. 25.Use a² − b² = (a + b)(a − b) to find 25² − 12².
26. 26.Use (a + b)(a − b) = a² − b² to find 47 × 33.
27. 27.Use (a − b)² = a² − 2ab + b² to find 52².
28. 28.Use (a − b)² = a² − 2ab + b² to find 48².
29. 29.Find the value of x² + 2xy + y² when x = 10 and y = 1.
30. 30.Find the value of x² + 2xy + y² when x = 14 and y = 4.
31. 31.Find the value of x² − 2xy + y² when x = 11 and y = 2.
32. 32.If a + b = 3 and ab = 2, what is a² + b²?
33. 33.Find the value of x² − 2xy + y² when x = 12 and y = 11.
34. 34.Use (a + b)² = a² + 2ab + b² to find 34².
35. 35.Use (a + b)² = a² + 2ab + b² to find 92².
36. 36.If a + b = 16 and ab = 60, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 61².
38. 38.Use (a − b)² = a² − 2ab + b² to find 13².
39. 39.Use (a + b)² = a² + 2ab + b² to find 18².
40. 40.Use (a − b)² = a² − 2ab + b² to find 33².

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