Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 487 · 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 = 2 and ab = 3, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 47².
3. 3.Use (a − b)² = a² − 2ab + b² to find 27².
4. 4.If a + b = 3 and ab = 2, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 101².
6. 6.Find the value of x² − y² when x = 11 and y = 8.
7. 7.Find the value of x² + 2xy + y² when x = 5 and y = 3.
8. 8.Use (a + b)(a − b) = a² − b² to find 41 × 39.
9. 9.Use (a + b)² = a² + 2ab + b² to find 85².
10. 10.Use (a − b)² = a² − 2ab + b² to find 38².
11. 11.Use a² − b² = (a + b)(a − b) to find 30² − 9².
12. 12.Use (a − b)² = a² − 2ab + b² to find 88².
13. 13.Use (a + b)² = a² + 2ab + b² to find 107².
14. 14.Use (a − b)² = a² − 2ab + b² to find 75².
15. 15.Use (a + b)² = a² + 2ab + b² to find 42².
16. 16.If a + b = 6 and ab = 8, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 91² − 73².
18. 18.Use (a + b)(a − b) = a² − b² to find 91 × 89.
19. 19.Use (a + b)(a − b) = a² − b² to find 96 × 84.
20. 20.Find the value of x² + 2xy + y² when x = 3 and y = 1.
21. 21.Use (a − b)² = a² − 2ab + b² to find 24².
22. 22.Use (a − b)² = a² − 2ab + b² to find 37².
23. 23.Find the value of x² − 2xy + y² when x = 4 and y = 2.
24. 24.Use a² − b² = (a + b)(a − b) to find 89² − 78².
25. 25.Use (a + b)² = a² + 2ab + b² to find 36².
26. 26.Use (a + b)(a − b) = a² − b² to find 82 × 78.
27. 27.Use a² − b² = (a + b)(a − b) to find 44² − 23².
28. 28.Use a² − b² = (a + b)(a − b) to find 22² − 3².
29. 29.Find the value of x² − y² when x = 3 and y = 1.
30. 30.If a + b = 4 and ab = 3, what is a² + b²?
31. 31.If a − b = 3 and ab = 10, what is a² + b²?
32. 32.Find the value of x² − y² when x = 12 and y = 9.
33. 33.Use (a + b)² = a² + 2ab + b² to find 88².
34. 34.Find the value of x² − 2xy + y² when x = 8 and y = 4.
35. 35.Find the value of x² + 2xy + y² when x = 4 and y = 2.
36. 36.Use (a + b)² = a² + 2ab + b² to find 98².
37. 37.Use (a + b)(a − b) = a² − b² to find 33 × 27.
38. 38.Use a² − b² = (a + b)(a − b) to find 36² − 14².
39. 39.Use (a + b)² = a² + 2ab + b² to find 28².
40. 40.Find the value of x² + 2xy + y² when x = 11 and y = 6.

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