Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 189 · 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 61².
2. 2.Find the value of x² + 2xy + y² when x = 5 and y = 4.
3. 3.Use (a − b)² = a² − 2ab + b² to find 23².
4. 4.If a − b = 9 and ab = 36, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 36² − 1².
6. 6.Use (a + b)(a − b) = a² − b² to find 44 × 36.
7. 7.If a + b = 12 and ab = 32, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 92² − 12².
9. 9.Use (a + b)(a − b) = a² − b² to find 51 × 49.
10. 10.Use a² − b² = (a + b)(a − b) to find 71² − 8².
11. 11.Find the value of x² − y² when x = 4 and y = 1.
12. 12.Find the value of x² + 2xy + y² when x = 13 and y = 9.
13. 13.If a + b = 7 and ab = 12, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 19².
15. 15.Use (a + b)² = a² + 2ab + b² to find 27².
16. 16.Use a² − b² = (a + b)(a − b) to find 59² − 8².
17. 17.Find the value of x² + 2xy + y² when x = 5 and y = 1.
18. 18.Use a² − b² = (a + b)(a − b) to find 41² − 37².
19. 19.Find the value of x² − y² when x = 4 and y = 2.
20. 20.Use (a + b)(a − b) = a² − b² to find 23 × 17.
21. 21.Use a² − b² = (a + b)(a − b) to find 56² − 10².
22. 22.Use (a + b)² = a² + 2ab + b² to find 28².
23. 23.Use (a + b)(a − b) = a² − b² to find 84 × 76.
24. 24.Use (a + b)² = a² + 2ab + b² to find 32².
25. 25.Find the value of x² + 2xy + y² when x = 8 and y = 5.
26. 26.Use a² − b² = (a + b)(a − b) to find 99² − 21².
27. 27.Use (a − b)² = a² − 2ab + b² to find 31².
28. 28.Find the value of x² − y² when x = 8 and y = 5.
29. 29.Use (a − b)² = a² − 2ab + b² to find 68².
30. 30.Use a² − b² = (a + b)(a − b) to find 79² − 8².
31. 31.Use (a − b)² = a² − 2ab + b² to find 97².
32. 32.Use (a + b)² = a² + 2ab + b² to find 93².
33. 33.Find the value of x² + 2xy + y² when x = 4 and y = 2.
34. 34.Use a² − b² = (a + b)(a − b) to find 46² − 44².
35. 35.Use (a + b)(a − b) = a² − b² to find 26 × 14.
36. 36.Use a² − b² = (a + b)(a − b) to find 76² − 14².
37. 37.Use (a + b)² = a² + 2ab + b² to find 71².
38. 38.Use (a + b)² = a² + 2ab + b² to find 59².
39. 39.If a + b = 11 and ab = 28, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 96 × 84.

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