Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 2 · 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.If a − b = 1 and ab = 2, what is a² + b²?
2. 2.Use (a + b)(a − b) = a² − b² to find 53 × 47.
3. 3.Find the value of x² − 2xy + y² when x = 8 and y = 3.
4. 4.Use a² − b² = (a + b)(a − b) to find 58² − 47².
5. 5.Find the value of x² − 2xy + y² when x = 14 and y = 5.
6. 6.Use (a + b)² = a² + 2ab + b² to find 38².
7. 7.Use (a + b)² = a² + 2ab + b² to find 109².
8. 8.Use a² − b² = (a + b)(a − b) to find 46² − 43².
9. 9.Use a² − b² = (a + b)(a − b) to find 52² − 15².
10. 10.If a + b = 8 and ab = 7, what is a² + b²?
11. 11.Find the value of x² − y² when x = 12 and y = 11.
12. 12.Find the value of x² − y² when x = 5 and y = 3.
13. 13.If a − b = 6 and ab = 16, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 17².
15. 15.Use (a − b)² = a² − 2ab + b² to find 98².
16. 16.Use (a + b)² = a² + 2ab + b² to find 32².
17. 17.Use (a − b)² = a² − 2ab + b² to find 76².
18. 18.Use (a − b)² = a² − 2ab + b² to find 46².
19. 19.Use (a − b)² = a² − 2ab + b² to find 82².
20. 20.Use a² − b² = (a + b)(a − b) to find 37² − 10².
21. 21.Use (a + b)² = a² + 2ab + b² to find 88².
22. 22.Use (a + b)(a − b) = a² − b² to find 64 × 56.
23. 23.Use (a + b)² = a² + 2ab + b² to find 92².
24. 24.Find the value of x² + 2xy + y² when x = 6 and y = 2.
25. 25.If a + b = 5 and ab = 6, what is a² + b²?
26. 26.If a − b = 5 and ab = 6, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 107².
28. 28.Use (a + b)² = a² + 2ab + b² to find 85².
29. 29.Use (a + b)² = a² + 2ab + b² to find 12².
30. 30.Use (a + b)² = a² + 2ab + b² to find 63².
31. 31.If a − b = 6 and ab = 72, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 29².
33. 33.Use (a + b)(a − b) = a² − b² to find 101 × 99.
34. 34.If a − b = 9 and ab = 36, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 99² − 12².
36. 36.Use (a + b)² = a² + 2ab + b² to find 16².
37. 37.Use (a + b)(a − b) = a² − b² to find 34 × 26.
38. 38.Use (a − b)² = a² − 2ab + b² to find 37².
39. 39.Use (a − b)² = a² − 2ab + b² to find 99².
40. 40.Find the value of x² + 2xy + y² when x = 4 and y = 3.

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