Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 660 · 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 36 × 24.
2. 2.Use (a − b)² = a² − 2ab + b² to find 27².
3. 3.Use (a − b)² = a² − 2ab + b² to find 37².
4. 4.Use (a − b)² = a² − 2ab + b² to find 45².
5. 5.Use a² − b² = (a + b)(a − b) to find 89² − 13².
6. 6.Use (a − b)² = a² − 2ab + b² to find 84².
7. 7.If a + b = 10 and ab = 9, what is a² + b²?
8. 8.If a − b = 5 and ab = 6, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 12².
10. 10.If a − b = 3 and ab = 10, what is a² + b²?
11. 11.Find the value of x² + 2xy + y² when x = 8 and y = 7.
12. 12.Use (a − b)² = a² − 2ab + b² to find 89².
13. 13.Use (a + b)² = a² + 2ab + b² to find 41².
14. 14.Use (a + b)(a − b) = a² − b² to find 61 × 59.
15. 15.Use (a + b)(a − b) = a² − b² to find 42 × 38.
16. 16.Use a² − b² = (a + b)(a − b) to find 91² − 15².
17. 17.If a + b = 3 and ab = 2, what is a² + b²?
18. 18.Use a² − b² = (a + b)(a − b) to find 36² − 9².
19. 19.If a − b = 1 and ab = 6, what is a² + b²?
20. 20.Find the value of x² + 2xy + y² when x = 3 and y = 2.
21. 21.Use a² − b² = (a + b)(a − b) to find 46² − 40².
22. 22.Find the value of x² − y² when x = 5 and y = 2.
23. 23.Find the value of x² + 2xy + y² when x = 13 and y = 12.
24. 24.Use (a + b)(a − b) = a² − b² to find 41 × 39.
25. 25.Use a² − b² = (a + b)(a − b) to find 92² − 91².
26. 26.Use (a + b)² = a² + 2ab + b² to find 51².
27. 27.Use (a + b)(a − b) = a² − b² to find 45 × 35.
28. 28.Use (a + b)² = a² + 2ab + b² to find 42².
29. 29.Find the value of x² + 2xy + y² when x = 12 and y = 11.
30. 30.Use (a + b)² = a² + 2ab + b² to find 32².
31. 31.Use (a + b)(a − b) = a² − b² to find 62 × 58.
32. 32.Use (a + b)² = a² + 2ab + b² to find 27².
33. 33.Use (a + b)² = a² + 2ab + b² to find 88².
34. 34.Use (a − b)² = a² − 2ab + b² to find 92².
35. 35.Use (a + b)² = a² + 2ab + b² to find 43².
36. 36.Use (a − b)² = a² − 2ab + b² to find 24².
37. 37.Use (a − b)² = a² − 2ab + b² to find 32².
38. 38.Use (a + b)² = a² + 2ab + b² to find 107².
39. 39.Use (a + b)² = a² + 2ab + b² to find 55².
40. 40.Find the value of x² − y² when x = 13 and y = 2.

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