Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 100 · 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)(a − b) = a² − b² to find 29 × 11.
2. 2.Use (a + b)(a − b) = a² − b² to find 87 × 73.
3. 3.Use a² − b² = (a + b)(a − b) to find 68² − 33².
4. 4.Find the value of x² − 2xy + y² when x = 9 and y = 7.
5. 5.Use (a + b)² = a² + 2ab + b² to find 53².
6. 6.Use (a + b)(a − b) = a² − b² to find 93 × 87.
7. 7.If a − b = 1 and ab = 56, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 37².
9. 9.Use (a + b)² = a² + 2ab + b² to find 88².
10. 10.If a + b = 3 and ab = 2, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 59² − 34².
12. 12.Use (a + b)² = a² + 2ab + b² to find 74².
13. 13.Find the value of x² + 2xy + y² when x = 3 and y = 1.
14. 14.If a − b = 4 and ab = 32, what is a² + b²?
15. 15.If a − b = 1 and ab = 110, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 82².
17. 17.Use a² − b² = (a + b)(a − b) to find 77² − 62².
18. 18.Use (a + b)² = a² + 2ab + b² to find 14².
19. 19.Find the value of x² − 2xy + y² when x = 4 and y = 2.
20. 20.Use (a − b)² = a² − 2ab + b² to find 85².
21. 21.Use (a − b)² = a² − 2ab + b² to find 95².
22. 22.Use (a − b)² = a² − 2ab + b² to find 33².
23. 23.Use (a − b)² = a² − 2ab + b² to find 88².
24. 24.Use (a + b)² = a² + 2ab + b² to find 43².
25. 25.Find the value of x² + 2xy + y² when x = 11 and y = 1.
26. 26.Use (a + b)(a − b) = a² − b² to find 43 × 37.
27. 27.Use (a − b)² = a² − 2ab + b² to find 39².
28. 28.Use (a + b)² = a² + 2ab + b² to find 55².
29. 29.Use a² − b² = (a + b)(a − b) to find 91² − 54².
30. 30.Use (a − b)² = a² − 2ab + b² to find 58².
31. 31.Find the value of x² − 2xy + y² when x = 9 and y = 2.
32. 32.Use (a + b)(a − b) = a² − b² to find 37 × 23.
33. 33.Use a² − b² = (a + b)(a − b) to find 65² − 13².
34. 34.Find the value of x² − y² when x = 9 and y = 2.
35. 35.Use (a + b)² = a² + 2ab + b² to find 57².
36. 36.Use (a + b)² = a² + 2ab + b² to find 34².
37. 37.Use a² − b² = (a + b)(a − b) to find 31² − 21².
38. 38.Use (a + b)² = a² + 2ab + b² to find 54².
39. 39.Use (a + b)² = a² + 2ab + b² to find 12².
40. 40.Find the value of x² + 2xy + y² when x = 10 and y = 6.

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