Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 827 · 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.If a + b = 12 and ab = 27, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 25².
3. 3.Use a² − b² = (a + b)(a − b) to find 21² − 11².
4. 4.Use (a + b)(a − b) = a² − b² to find 44 × 36.
5. 5.Use (a + b)(a − b) = a² − b² to find 28 × 12.
6. 6.Use (a − b)² = a² − 2ab + b² to find 61².
7. 7.Use (a + b)² = a² + 2ab + b² to find 34².
8. 8.Use (a + b)² = a² + 2ab + b² to find 73².
9. 9.Use (a − b)² = a² − 2ab + b² to find 21².
10. 10.Use (a − b)² = a² − 2ab + b² to find 98².
11. 11.Use (a + b)² = a² + 2ab + b² to find 52².
12. 12.Use (a + b)² = a² + 2ab + b² to find 108².
13. 13.If a + b = 14 and ab = 24, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 23².
15. 15.Find the value of x² − y² when x = 8 and y = 7.
16. 16.Use (a − b)² = a² − 2ab + b² to find 91².
17. 17.If a − b = 1 and ab = 2, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 26 × 14.
19. 19.Find the value of x² − 2xy + y² when x = 12 and y = 11.
20. 20.Find the value of x² − 2xy + y² when x = 7 and y = 1.
21. 21.Use (a + b)(a − b) = a² − b² to find 29 × 11.
22. 22.Use (a + b)(a − b) = a² − b² to find 99 × 81.
23. 23.Use (a + b)² = a² + 2ab + b² to find 74².
24. 24.If a − b = 2 and ab = 35, what is a² + b²?
25. 25.Find the value of x² − y² when x = 4 and y = 1.
26. 26.If a − b = 9 and ab = 10, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 45².
28. 28.Use (a − b)² = a² − 2ab + b² to find 66².
29. 29.If a + b = 10 and ab = 24, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 41².
31. 31.Find the value of x² + 2xy + y² when x = 15 and y = 8.
32. 32.Use a² − b² = (a + b)(a − b) to find 53² − 6².
33. 33.If a − b = 5 and ab = 36, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 54².
35. 35.Find the value of x² + 2xy + y² when x = 3 and y = 2.
36. 36.Use (a + b)(a − b) = a² − b² to find 59 × 41.
37. 37.Use (a + b)² = a² + 2ab + b² to find 39².
38. 38.Use (a + b)(a − b) = a² − b² to find 92 × 88.
39. 39.Find the value of x² + 2xy + y² when x = 4 and y = 1.
40. 40.Use (a − b)² = a² − 2ab + b² to find 62².

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