Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 40 · 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.Find the value of x² − 2xy + y² when x = 4 and y = 2.
2. 2.Use (a + b)(a − b) = a² − b² to find 92 × 88.
3. 3.Find the value of x² + 2xy + y² when x = 8 and y = 6.
4. 4.If a + b = 3 and ab = 2, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 77².
6. 6.Use (a + b)(a − b) = a² − b² to find 55 × 45.
7. 7.Use a² − b² = (a + b)(a − b) to find 96² − 50².
8. 8.Use (a − b)² = a² − 2ab + b² to find 58².
9. 9.Use (a − b)² = a² − 2ab + b² to find 66².
10. 10.Find the value of x² + 2xy + y² when x = 14 and y = 3.
11. 11.Use a² − b² = (a + b)(a − b) to find 72² − 70².
12. 12.Find the value of x² + 2xy + y² when x = 6 and y = 3.
13. 13.If a + b = 15 and ab = 44, what is a² + b²?
14. 14.Find the value of x² − 2xy + y² when x = 5 and y = 4.
15. 15.Use a² − b² = (a + b)(a − b) to find 36² − 30².
16. 16.If a + b = 5 and ab = 6, what is a² + b²?
17. 17.Use (a + b)(a − b) = a² − b² to find 82 × 78.
18. 18.Use a² − b² = (a + b)(a − b) to find 36² − 27².
19. 19.Find the value of x² + 2xy + y² when x = 9 and y = 6.
20. 20.Use a² − b² = (a + b)(a − b) to find 88² − 23².
21. 21.Use (a + b)² = a² + 2ab + b² to find 94².
22. 22.Use (a + b)(a − b) = a² − b² to find 101 × 99.
23. 23.Use (a + b)(a − b) = a² − b² to find 72 × 68.
24. 24.Use (a + b)(a − b) = a² − b² to find 54 × 46.
25. 25.If a − b = 5 and ab = 50, what is a² + b²?
26. 26.If a + b = 6 and ab = 8, what is a² + b²?
27. 27.If a + b = 10 and ab = 9, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 21².
29. 29.Find the value of x² − 2xy + y² when x = 7 and y = 1.
30. 30.Use a² − b² = (a + b)(a − b) to find 50² − 21².
31. 31.If a − b = 3 and ab = 40, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 47².
33. 33.Use (a + b)(a − b) = a² − b² to find 25 × 15.
34. 34.Use (a + b)² = a² + 2ab + b² to find 34².
35. 35.Use (a + b)(a − b) = a² − b² to find 53 × 47.
36. 36.Use a² − b² = (a + b)(a − b) to find 86² − 22².
37. 37.If a − b = 1 and ab = 12, what is a² + b²?
38. 38.Find the value of x² − 2xy + y² when x = 4 and y = 1.
39. 39.Use a² − b² = (a + b)(a − b) to find 94² − 8².
40. 40.Use a² − b² = (a + b)(a − b) to find 78² − 69².

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