Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 568 · 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 a² − b² = (a + b)(a − b) to find 92² − 75².
2. 2.Find the value of x² + 2xy + y² when x = 10 and y = 6.
3. 3.If a + b = 3 and ab = 2, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 67².
5. 5.Use (a + b)(a − b) = a² − b² to find 71 × 69.
6. 6.Use (a + b)(a − b) = a² − b² to find 106 × 94.
7. 7.Use a² − b² = (a + b)(a − b) to find 39² − 32².
8. 8.If a − b = 1 and ab = 72, what is a² + b²?
9. 9.Use (a − b)² = a² − 2ab + b² to find 55².
10. 10.Use (a − b)² = a² − 2ab + b² to find 11².
11. 11.Find the value of x² − y² when x = 5 and y = 3.
12. 12.Use a² − b² = (a + b)(a − b) to find 42² − 32².
13. 13.If a + b = 7 and ab = 12, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 91².
15. 15.If a + b = 13 and ab = 42, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 95 × 85.
17. 17.Use (a + b)² = a² + 2ab + b² to find 78².
18. 18.Use (a + b)² = a² + 2ab + b² to find 65².
19. 19.If a + b = 9 and ab = 8, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 50² − 15².
21. 21.Find the value of x² + 2xy + y² when x = 13 and y = 3.
22. 22.Find the value of x² − y² when x = 8 and y = 1.
23. 23.Use (a + b)(a − b) = a² − b² to find 37 × 23.
24. 24.Use (a + b)(a − b) = a² − b² to find 56 × 44.
25. 25.Use (a + b)(a − b) = a² − b² to find 51 × 49.
26. 26.Use (a + b)² = a² + 2ab + b² to find 42².
27. 27.Find the value of x² − 2xy + y² when x = 3 and y = 2.
28. 28.Use (a + b)(a − b) = a² − b² to find 65 × 55.
29. 29.Use a² − b² = (a + b)(a − b) to find 86² − 82².
30. 30.If a − b = 1 and ab = 132, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 81².
32. 32.If a − b = 4 and ab = 60, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 35².
34. 34.Use (a + b)² = a² + 2ab + b² to find 58².
35. 35.Use (a − b)² = a² − 2ab + b² to find 52².
36. 36.If a + b = 5 and ab = 6, what is a² + b²?
37. 37.If a + b = 17 and ab = 72, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 19².
39. 39.Use (a − b)² = a² − 2ab + b² to find 12².
40. 40.Use (a + b)² = a² + 2ab + b² to find 16².

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