Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 62 · 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 75².
2. 2.Find the value of x² − y² when x = 12 and y = 6.
3. 3.Find the value of x² − 2xy + y² when x = 8 and y = 7.
4. 4.Use a² − b² = (a + b)(a − b) to find 25² − 24².
5. 5.If a + b = 7 and ab = 12, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 87².
7. 7.Use (a + b)(a − b) = a² − b² to find 101 × 99.
8. 8.Use (a + b)² = a² + 2ab + b² to find 22².
9. 9.Use (a + b)² = a² + 2ab + b² to find 32².
10. 10.Use (a − b)² = a² − 2ab + b² to find 44².
11. 11.Use (a + b)(a − b) = a² − b² to find 45 × 35.
12. 12.Use (a − b)² = a² − 2ab + b² to find 56².
13. 13.Use (a − b)² = a² − 2ab + b² to find 48².
14. 14.Find the value of x² − y² when x = 6 and y = 1.
15. 15.Use (a + b)² = a² + 2ab + b² to find 31².
16. 16.Use (a + b)(a − b) = a² − b² to find 92 × 88.
17. 17.Use a² − b² = (a + b)(a − b) to find 46² − 38².
18. 18.Use (a − b)² = a² − 2ab + b² to find 84².
19. 19.Use (a + b)² = a² + 2ab + b² to find 63².
20. 20.Find the value of x² − 2xy + y² when x = 6 and y = 5.
21. 21.Use a² − b² = (a + b)(a − b) to find 45² − 39².
22. 22.Use a² − b² = (a + b)(a − b) to find 84² − 14².
23. 23.Use (a + b)² = a² + 2ab + b² to find 83².
24. 24.Use (a − b)² = a² − 2ab + b² to find 38².
25. 25.If a + b = 3 and ab = 2, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 65².
27. 27.Use (a + b)² = a² + 2ab + b² to find 61².
28. 28.Use (a + b)(a − b) = a² − b² to find 104 × 96.
29. 29.Use a² − b² = (a + b)(a − b) to find 48² − 11².
30. 30.Find the value of x² − y² when x = 6 and y = 3.
31. 31.Use (a + b)(a − b) = a² − b² to find 93 × 87.
32. 32.Use a² − b² = (a + b)(a − b) to find 42² − 7².
33. 33.Find the value of x² + 2xy + y² when x = 11 and y = 4.
34. 34.Find the value of x² − y² when x = 13 and y = 1.
35. 35.Use (a + b)(a − b) = a² − b² to find 49 × 31.
36. 36.Find the value of x² + 2xy + y² when x = 10 and y = 3.
37. 37.Use (a − b)² = a² − 2ab + b² to find 91².
38. 38.Use (a + b)(a − b) = a² − b² to find 63 × 57.
39. 39.Use a² − b² = (a + b)(a − b) to find 32² − 2².
40. 40.Use (a + b)² = a² + 2ab + b² to find 45².

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