Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 290 · 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 44 × 36.
2. 2.Use (a + b)(a − b) = a² − b² to find 73 × 67.
3. 3.Use a² − b² = (a + b)(a − b) to find 37² − 7².
4. 4.Use (a − b)² = a² − 2ab + b² to find 96².
5. 5.Use (a + b)² = a² + 2ab + b² to find 28².
6. 6.If a − b = 1 and ab = 2, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 98².
8. 8.Use a² − b² = (a + b)(a − b) to find 81² − 31².
9. 9.Find the value of x² − 2xy + y² when x = 14 and y = 1.
10. 10.Use (a − b)² = a² − 2ab + b² to find 63².
11. 11.Use (a + b)(a − b) = a² − b² to find 24 × 16.
12. 12.Use (a + b)(a − b) = a² − b² to find 59 × 41.
13. 13.If a − b = 1 and ab = 20, what is a² + b²?
14. 14.If a + b = 6 and ab = 5, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 59².
16. 16.If a − b = 5 and ab = 14, what is a² + b²?
17. 17.If a − b = 4 and ab = 96, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 72 × 68.
19. 19.Find the value of x² − 2xy + y² when x = 3 and y = 2.
20. 20.Find the value of x² − 2xy + y² when x = 8 and y = 6.
21. 21.Use (a − b)² = a² − 2ab + b² to find 52².
22. 22.Find the value of x² + 2xy + y² when x = 12 and y = 9.
23. 23.Use (a + b)² = a² + 2ab + b² to find 58².
24. 24.Find the value of x² − 2xy + y² when x = 9 and y = 3.
25. 25.Use (a + b)(a − b) = a² − b² to find 36 × 24.
26. 26.Find the value of x² + 2xy + y² when x = 11 and y = 8.
27. 27.Find the value of x² − y² when x = 14 and y = 7.
28. 28.If a + b = 15 and ab = 56, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 107 × 93.
30. 30.If a − b = 6 and ab = 27, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 37².
32. 32.Find the value of x² − y² when x = 7 and y = 4.
33. 33.Use (a + b)² = a² + 2ab + b² to find 18².
34. 34.Find the value of x² − 2xy + y² when x = 7 and y = 4.
35. 35.Find the value of x² − y² when x = 9 and y = 7.
36. 36.Use a² − b² = (a + b)(a − b) to find 64² − 17².
37. 37.Use a² − b² = (a + b)(a − b) to find 80² − 18².
38. 38.Use a² − b² = (a + b)(a − b) to find 28² − 15².
39. 39.Use (a − b)² = a² − 2ab + b² to find 88².
40. 40.If a − b = 2 and ab = 120, what is a² + b²?

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