Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 493 · 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.Find the value of x² − y² when x = 8 and y = 2.
2. 2.Use (a + b)(a − b) = a² − b² to find 35 × 25.
3. 3.Use (a + b)² = a² + 2ab + b² to find 75².
4. 4.Use a² − b² = (a + b)(a − b) to find 70² − 57².
5. 5.Use (a + b)(a − b) = a² − b² to find 92 × 88.
6. 6.Use (a − b)² = a² − 2ab + b² to find 78².
7. 7.Find the value of x² − y² when x = 4 and y = 1.
8. 8.Use (a + b)(a − b) = a² − b² to find 79 × 61.
9. 9.Use a² − b² = (a + b)(a − b) to find 44² − 38².
10. 10.Find the value of x² − 2xy + y² when x = 3 and y = 2.
11. 11.Use (a − b)² = a² − 2ab + b² to find 28².
12. 12.If a − b = 4 and ab = 60, what is a² + b²?
13. 13.Find the value of x² − 2xy + y² when x = 8 and y = 4.
14. 14.Use (a + b)² = a² + 2ab + b² to find 51².
15. 15.If a + b = 4 and ab = 3, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 97² − 70².
17. 17.Use (a − b)² = a² − 2ab + b² to find 14².
18. 18.Use (a + b)² = a² + 2ab + b² to find 101².
19. 19.Use a² − b² = (a + b)(a − b) to find 68² − 60².
20. 20.Use a² − b² = (a + b)(a − b) to find 20² − 1².
21. 21.Use (a + b)(a − b) = a² − b² to find 104 × 96.
22. 22.Find the value of x² − 2xy + y² when x = 9 and y = 2.
23. 23.Use (a − b)² = a² − 2ab + b² to find 29².
24. 24.Use (a + b)² = a² + 2ab + b² to find 33².
25. 25.Use (a − b)² = a² − 2ab + b² to find 13².
26. 26.Use (a − b)² = a² − 2ab + b² to find 58².
27. 27.Use (a + b)² = a² + 2ab + b² to find 81².
28. 28.Use (a − b)² = a² − 2ab + b² to find 67².
29. 29.Find the value of x² − 2xy + y² when x = 3 and y = 1.
30. 30.Use a² − b² = (a + b)(a − b) to find 72² − 13².
31. 31.Use (a + b)(a − b) = a² − b² to find 42 × 38.
32. 32.Use (a + b)² = a² + 2ab + b² to find 87².
33. 33.Use (a + b)² = a² + 2ab + b² to find 108².
34. 34.Use (a − b)² = a² − 2ab + b² to find 94².
35. 35.If a − b = 4 and ab = 12, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 31².
37. 37.Find the value of x² − 2xy + y² when x = 15 and y = 10.
38. 38.Use (a + b)(a − b) = a² − b² to find 86 × 74.
39. 39.Find the value of x² − y² when x = 7 and y = 1.
40. 40.Use (a + b)(a − b) = a² − b² to find 103 × 97.

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