Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 801 · 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 78 × 62.
2. 2.If a − b = 1 and ab = 12, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 22².
4. 4.Find the value of x² + 2xy + y² when x = 3 and y = 1.
5. 5.Use a² − b² = (a + b)(a − b) to find 90² − 85².
6. 6.Use (a + b)² = a² + 2ab + b² to find 102².
7. 7.Use (a + b)(a − b) = a² − b² to find 63 × 57.
8. 8.If a + b = 11 and ab = 24, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 27² − 12².
10. 10.Use (a − b)² = a² − 2ab + b² to find 91².
11. 11.Find the value of x² + 2xy + y² when x = 7 and y = 1.
12. 12.Use a² − b² = (a + b)(a − b) to find 30² − 19².
13. 13.If a + b = 7 and ab = 10, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 90² − 36².
15. 15.Use a² − b² = (a + b)(a − b) to find 41² − 28².
16. 16.Find the value of x² + 2xy + y² when x = 5 and y = 3.
17. 17.Use (a + b)² = a² + 2ab + b² to find 99².
18. 18.Find the value of x² − y² when x = 7 and y = 1.
19. 19.Find the value of x² − 2xy + y² when x = 4 and y = 2.
20. 20.If a − b = 2 and ab = 15, what is a² + b²?
21. 21.Find the value of x² − y² when x = 6 and y = 4.
22. 22.Use (a + b)(a − b) = a² − b² to find 26 × 14.
23. 23.Use a² − b² = (a + b)(a − b) to find 87² − 11².
24. 24.Find the value of x² − y² when x = 12 and y = 8.
25. 25.Find the value of x² − y² when x = 9 and y = 4.
26. 26.Use (a + b)² = a² + 2ab + b² to find 67².
27. 27.Find the value of x² − 2xy + y² when x = 7 and y = 4.
28. 28.Use a² − b² = (a + b)(a − b) to find 58² − 15².
29. 29.Find the value of x² + 2xy + y² when x = 5 and y = 1.
30. 30.Use (a − b)² = a² − 2ab + b² to find 97².
31. 31.Use a² − b² = (a + b)(a − b) to find 77² − 70².
32. 32.Use (a + b)(a − b) = a² − b² to find 77 × 63.
33. 33.Use (a − b)² = a² − 2ab + b² to find 77².
34. 34.Use a² − b² = (a + b)(a − b) to find 97² − 1².
35. 35.Use (a + b)(a − b) = a² − b² to find 95 × 85.
36. 36.Use (a + b)(a − b) = a² − b² to find 101 × 99.
37. 37.Use (a + b)² = a² + 2ab + b² to find 21².
38. 38.Use (a + b)² = a² + 2ab + b² to find 83².
39. 39.Use (a − b)² = a² − 2ab + b² to find 69².
40. 40.Use (a + b)(a − b) = a² − b² to find 62 × 58.

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