Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 409 · 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 39² − 24².
2. 2.Use (a − b)² = a² − 2ab + b² to find 11².
3. 3.Use (a + b)(a − b) = a² − b² to find 58 × 42.
4. 4.Use (a − b)² = a² − 2ab + b² to find 61².
5. 5.Use a² − b² = (a + b)(a − b) to find 88² − 78².
6. 6.Use (a + b)² = a² + 2ab + b² to find 61².
7. 7.Use (a + b)² = a² + 2ab + b² to find 55².
8. 8.Find the value of x² − 2xy + y² when x = 3 and y = 2.
9. 9.Use (a + b)(a − b) = a² − b² to find 101 × 99.
10. 10.Use a² − b² = (a + b)(a − b) to find 77² − 36².
11. 11.Use (a + b)² = a² + 2ab + b² to find 58².
12. 12.Use (a + b)(a − b) = a² − b² to find 77 × 63.
13. 13.If a + b = 8 and ab = 15, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 27² − 1².
15. 15.Use (a + b)(a − b) = a² − b² to find 71 × 69.
16. 16.Use (a − b)² = a² − 2ab + b² to find 91².
17. 17.Use (a − b)² = a² − 2ab + b² to find 89².
18. 18.If a + b = 10 and ab = 16, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 62².
20. 20.Use a² − b² = (a + b)(a − b) to find 39² − 28².
21. 21.Use (a + b)² = a² + 2ab + b² to find 52².
22. 22.Find the value of x² + 2xy + y² when x = 7 and y = 5.
23. 23.Use (a + b)(a − b) = a² − b² to find 109 × 91.
24. 24.Use (a + b)² = a² + 2ab + b² to find 18².
25. 25.Find the value of x² + 2xy + y² when x = 10 and y = 9.
26. 26.Use (a + b)² = a² + 2ab + b² to find 97².
27. 27.Use (a + b)² = a² + 2ab + b² to find 81².
28. 28.Find the value of x² + 2xy + y² when x = 3 and y = 2.
29. 29.Use (a − b)² = a² − 2ab + b² to find 25².
30. 30.Find the value of x² − 2xy + y² when x = 15 and y = 5.
31. 31.Find the value of x² − y² when x = 10 and y = 3.
32. 32.Use a² − b² = (a + b)(a − b) to find 77² − 64².
33. 33.Use a² − b² = (a + b)(a − b) to find 96² − 42².
34. 34.Find the value of x² − 2xy + y² when x = 4 and y = 1.
35. 35.Use (a + b)² = a² + 2ab + b² to find 28².
36. 36.Use (a + b)² = a² + 2ab + b² to find 99².
37. 37.Find the value of x² + 2xy + y² when x = 13 and y = 2.
38. 38.Use (a − b)² = a² − 2ab + b² to find 47².
39. 39.If a + b = 11 and ab = 28, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 47 × 33.

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