Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 4 · 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 = 8 and ab = 12, what is a² + b²?
2. 2.Use (a + b)(a − b) = a² − b² to find 85 × 75.
3. 3.Use (a − b)² = a² − 2ab + b² to find 31².
4. 4.Find the value of x² − y² when x = 7 and y = 3.
5. 5.Use (a − b)² = a² − 2ab + b² to find 87².
6. 6.Use (a + b)(a − b) = a² − b² to find 57 × 43.
7. 7.Use a² − b² = (a + b)(a − b) to find 61² − 3².
8. 8.Use (a − b)² = a² − 2ab + b² to find 56².
9. 9.Use (a − b)² = a² − 2ab + b² to find 98².
10. 10.Find the value of x² − y² when x = 12 and y = 5.
11. 11.Find the value of x² − 2xy + y² when x = 4 and y = 3.
12. 12.If a + b = 10 and ab = 9, what is a² + b²?
13. 13.Use (a + b)(a − b) = a² − b² to find 86 × 74.
14. 14.Use a² − b² = (a + b)(a − b) to find 40² − 29².
15. 15.Use a² − b² = (a + b)(a − b) to find 94² − 53².
16. 16.Use (a + b)² = a² + 2ab + b² to find 52².
17. 17.Use a² − b² = (a + b)(a − b) to find 41² − 7².
18. 18.Use (a + b)(a − b) = a² − b² to find 22 × 18.
19. 19.Use (a + b)² = a² + 2ab + b² to find 75².
20. 20.Use (a + b)² = a² + 2ab + b² to find 57².
21. 21.Find the value of x² + 2xy + y² when x = 15 and y = 4.
22. 22.If a − b = 3 and ab = 4, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 54² − 31².
24. 24.If a − b = 2 and ab = 3, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 69².
26. 26.Use (a + b)(a − b) = a² − b² to find 46 × 34.
27. 27.Use (a − b)² = a² − 2ab + b² to find 79².
28. 28.Use (a + b)² = a² + 2ab + b² to find 79².
29. 29.Use (a − b)² = a² − 2ab + b² to find 18².
30. 30.Find the value of x² − 2xy + y² when x = 4 and y = 1.
31. 31.Use (a − b)² = a² − 2ab + b² to find 58².
32. 32.Use (a + b)(a − b) = a² − b² to find 32 × 28.
33. 33.Use a² − b² = (a + b)(a − b) to find 80² − 65².
34. 34.Use (a − b)² = a² − 2ab + b² to find 62².
35. 35.Use (a + b)(a − b) = a² − b² to find 65 × 55.
36. 36.Use a² − b² = (a + b)(a − b) to find 38² − 31².
37. 37.If a + b = 3 and ab = 2, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 87 × 73.
39. 39.Find the value of x² − 2xy + y² when x = 10 and y = 6.
40. 40.If a − b = 4 and ab = 77, what is a² + b²?

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