Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 291 · 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 41².
2. 2.Use (a + b)² = a² + 2ab + b² to find 24².
3. 3.If a − b = 4 and ab = 12, what is a² + b²?
4. 4.Find the value of x² + 2xy + y² when x = 7 and y = 3.
5. 5.Find the value of x² − 2xy + y² when x = 14 and y = 13.
6. 6.Use a² − b² = (a + b)(a − b) to find 42² − 40².
7. 7.If a + b = 23 and ab = 132, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 62².
9. 9.Use (a + b)(a − b) = a² − b² to find 48 × 32.
10. 10.If a − b = 5 and ab = 50, what is a² + b²?
11. 11.Find the value of x² − y² when x = 15 and y = 12.
12. 12.Use (a + b)² = a² + 2ab + b² to find 45².
13. 13.If a + b = 10 and ab = 16, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 68².
15. 15.Use (a + b)² = a² + 2ab + b² to find 81².
16. 16.Use (a + b)² = a² + 2ab + b² to find 13².
17. 17.Use a² − b² = (a + b)(a − b) to find 72² − 43².
18. 18.Use a² − b² = (a + b)(a − b) to find 91² − 63².
19. 19.Use (a + b)² = a² + 2ab + b² to find 12².
20. 20.Use a² − b² = (a + b)(a − b) to find 96² − 42².
21. 21.Use (a − b)² = a² − 2ab + b² to find 93².
22. 22.If a − b = 3 and ab = 4, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 88² − 37².
24. 24.Use (a − b)² = a² − 2ab + b² to find 15².
25. 25.Use (a + b)(a − b) = a² − b² to find 95 × 85.
26. 26.Use (a − b)² = a² − 2ab + b² to find 44².
27. 27.Use (a + b)² = a² + 2ab + b² to find 88².
28. 28.Use (a − b)² = a² − 2ab + b² to find 28².
29. 29.Use (a + b)(a − b) = a² − b² to find 99 × 81.
30. 30.Use (a − b)² = a² − 2ab + b² to find 23².
31. 31.If a + b = 9 and ab = 18, what is a² + b²?
32. 32.If a + b = 5 and ab = 6, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 91² − 71².
34. 34.If a − b = 4 and ab = 5, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 36² − 13².
36. 36.Use (a − b)² = a² − 2ab + b² to find 59².
37. 37.Use (a − b)² = a² − 2ab + b² to find 43².
38. 38.Use (a − b)² = a² − 2ab + b² to find 39².
39. 39.Use (a + b)(a − b) = a² − b² to find 21 × 19.
40. 40.Find the value of x² − y² when x = 5 and y = 1.

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