Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 235 · 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 63².
2. 2.Use a² − b² = (a + b)(a − b) to find 72² − 44².
3. 3.Use a² − b² = (a + b)(a − b) to find 63² − 6².
4. 4.Use a² − b² = (a + b)(a − b) to find 91² − 59².
5. 5.If a + b = 3 and ab = 2, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 60² − 4².
7. 7.If a − b = 7 and ab = 60, what is a² + b²?
8. 8.Find the value of x² + 2xy + y² when x = 15 and y = 8.
9. 9.Use a² − b² = (a + b)(a − b) to find 23² − 22².
10. 10.Use (a + b)(a − b) = a² − b² to find 106 × 94.
11. 11.Use (a − b)² = a² − 2ab + b² to find 31².
12. 12.Find the value of x² − 2xy + y² when x = 8 and y = 7.
13. 13.Use (a + b)(a − b) = a² − b² to find 102 × 98.
14. 14.Use (a − b)² = a² − 2ab + b² to find 93².
15. 15.Use a² − b² = (a + b)(a − b) to find 72² − 53².
16. 16.Use (a + b)² = a² + 2ab + b² to find 45².
17. 17.Use (a − b)² = a² − 2ab + b² to find 21².
18. 18.If a − b = 6 and ab = 27, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 41².
20. 20.Use (a + b)(a − b) = a² − b² to find 56 × 44.
21. 21.Use (a − b)² = a² − 2ab + b² to find 33².
22. 22.Use (a + b)(a − b) = a² − b² to find 26 × 14.
23. 23.Use (a − b)² = a² − 2ab + b² to find 92².
24. 24.Use (a − b)² = a² − 2ab + b² to find 19².
25. 25.Use (a + b)² = a² + 2ab + b² to find 73².
26. 26.Use a² − b² = (a + b)(a − b) to find 62² − 60².
27. 27.Use (a − b)² = a² − 2ab + b² to find 83².
28. 28.Find the value of x² − 2xy + y² when x = 13 and y = 12.
29. 29.Use (a + b)(a − b) = a² − b² to find 65 × 55.
30. 30.Use a² − b² = (a + b)(a − b) to find 33² − 17².
31. 31.Use a² − b² = (a + b)(a − b) to find 77² − 46².
32. 32.Use (a + b)(a − b) = a² − b² to find 42 × 38.
33. 33.Use (a + b)(a − b) = a² − b² to find 27 × 13.
34. 34.Find the value of x² − y² when x = 13 and y = 10.
35. 35.Find the value of x² + 2xy + y² when x = 3 and y = 2.
36. 36.If a − b = 4 and ab = 21, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 47² − 14².
38. 38.Use (a + b)² = a² + 2ab + b² to find 18².
39. 39.Use (a + b)² = a² + 2ab + b² to find 34².
40. 40.Use (a + b)² = a² + 2ab + b² to find 32².

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