Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 918 · 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)(a − b) = a² − b² to find 24 × 16.
2. 2.Use a² − b² = (a + b)(a − b) to find 47² − 18².
3. 3.If a − b = 6 and ab = 72, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 63².
5. 5.Use a² − b² = (a + b)(a − b) to find 93² − 41².
6. 6.Use a² − b² = (a + b)(a − b) to find 55² − 28².
7. 7.Use (a + b)² = a² + 2ab + b² to find 57².
8. 8.Use a² − b² = (a + b)(a − b) to find 75² − 31².
9. 9.Use (a − b)² = a² − 2ab + b² to find 31².
10. 10.If a + b = 5 and ab = 6, what is a² + b²?
11. 11.Find the value of x² − 2xy + y² when x = 15 and y = 11.
12. 12.Use (a − b)² = a² − 2ab + b² to find 16².
13. 13.Use a² − b² = (a + b)(a − b) to find 91² − 25².
14. 14.Use a² − b² = (a + b)(a − b) to find 38² − 15².
15. 15.Find the value of x² − y² when x = 13 and y = 4.
16. 16.Find the value of x² + 2xy + y² when x = 5 and y = 2.
17. 17.Use (a + b)² = a² + 2ab + b² to find 58².
18. 18.Use (a − b)² = a² − 2ab + b² to find 26².
19. 19.Find the value of x² − 2xy + y² when x = 6 and y = 1.
20. 20.Use (a + b)² = a² + 2ab + b² to find 17².
21. 21.Use a² − b² = (a + b)(a − b) to find 35² − 7².
22. 22.Use (a + b)² = a² + 2ab + b² to find 69².
23. 23.Use (a − b)² = a² − 2ab + b² to find 91².
24. 24.Use (a − b)² = a² − 2ab + b² to find 33².
25. 25.Use (a + b)² = a² + 2ab + b² to find 23².
26. 26.Use (a + b)² = a² + 2ab + b² to find 73².
27. 27.If a + b = 4 and ab = 3, what is a² + b²?
28. 28.Find the value of x² + 2xy + y² when x = 5 and y = 3.
29. 29.Use a² − b² = (a + b)(a − b) to find 41² − 33².
30. 30.Use (a + b)(a − b) = a² − b² to find 72 × 68.
31. 31.If a − b = 7 and ab = 60, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 82².
33. 33.Use (a + b)(a − b) = a² − b² to find 33 × 27.
34. 34.Use a² − b² = (a + b)(a − b) to find 47² − 34².
35. 35.Find the value of x² + 2xy + y² when x = 9 and y = 2.
36. 36.Use (a + b)² = a² + 2ab + b² to find 98².
37. 37.Use a² − b² = (a + b)(a − b) to find 85² − 16².
38. 38.Use (a − b)² = a² − 2ab + b² to find 62².
39. 39.If a − b = 4 and ab = 5, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 72².

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