Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 551 · 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 46².
2. 2.Use (a + b)² = a² + 2ab + b² to find 59².
3. 3.Use a² − b² = (a + b)(a − b) to find 93² − 29².
4. 4.Use (a − b)² = a² − 2ab + b² to find 69².
5. 5.If a + b = 13 and ab = 12, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 34².
7. 7.Use (a − b)² = a² − 2ab + b² to find 61².
8. 8.Use (a + b)(a − b) = a² − b² to find 69 × 51.
9. 9.Use (a + b)(a − b) = a² − b² to find 23 × 17.
10. 10.Find the value of x² + 2xy + y² when x = 14 and y = 7.
11. 11.Use a² − b² = (a + b)(a − b) to find 85² − 33².
12. 12.Use (a − b)² = a² − 2ab + b² to find 92².
13. 13.If a − b = 3 and ab = 10, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 39².
15. 15.Find the value of x² + 2xy + y² when x = 10 and y = 1.
16. 16.Find the value of x² − y² when x = 13 and y = 3.
17. 17.Find the value of x² − 2xy + y² when x = 4 and y = 3.
18. 18.If a + b = 9 and ab = 18, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 49² − 45².
20. 20.Use (a − b)² = a² − 2ab + b² to find 85².
21. 21.If a − b = 1 and ab = 42, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 68 × 52.
23. 23.Find the value of x² + 2xy + y² when x = 15 and y = 3.
24. 24.Use a² − b² = (a + b)(a − b) to find 76² − 75².
25. 25.If a − b = 6 and ab = 27, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 81² − 12².
27. 27.Find the value of x² − y² when x = 9 and y = 8.
28. 28.Use (a + b)(a − b) = a² − b² to find 32 × 28.
29. 29.Use (a + b)(a − b) = a² − b² to find 27 × 13.
30. 30.Use a² − b² = (a + b)(a − b) to find 70² − 14².
31. 31.If a + b = 15 and ab = 36, what is a² + b²?
32. 32.Find the value of x² + 2xy + y² when x = 4 and y = 2.
33. 33.Use (a − b)² = a² − 2ab + b² to find 39².
34. 34.Use a² − b² = (a + b)(a − b) to find 38² − 10².
35. 35.Find the value of x² − y² when x = 8 and y = 3.
36. 36.Use (a + b)(a − b) = a² − b² to find 57 × 43.
37. 37.Use (a + b)(a − b) = a² − b² to find 107 × 93.
38. 38.Use a² − b² = (a + b)(a − b) to find 84² − 60².
39. 39.Use (a + b)² = a² + 2ab + b² to find 83².
40. 40.Use (a − b)² = a² − 2ab + b² to find 67².

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