Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 405 · 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 a² − b² = (a + b)(a − b) to find 96² − 33².
2. 2.Find the value of x² − y² when x = 12 and y = 9.
3. 3.Use (a + b)² = a² + 2ab + b² to find 13².
4. 4.Use (a + b)² = a² + 2ab + b² to find 27².
5. 5.Find the value of x² − 2xy + y² when x = 12 and y = 5.
6. 6.If a − b = 3 and ab = 4, what is a² + b²?
7. 7.Find the value of x² + 2xy + y² when x = 7 and y = 4.
8. 8.Use a² − b² = (a + b)(a − b) to find 55² − 53².
9. 9.Use (a + b)² = a² + 2ab + b² to find 74².
10. 10.Find the value of x² − y² when x = 6 and y = 1.
11. 11.Use (a + b)(a − b) = a² − b² to find 48 × 32.
12. 12.Use (a + b)² = a² + 2ab + b² to find 32².
13. 13.Use (a − b)² = a² − 2ab + b² to find 91².
14. 14.If a − b = 5 and ab = 66, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 41² − 36².
16. 16.Use a² − b² = (a + b)(a − b) to find 25² − 1².
17. 17.Use (a − b)² = a² − 2ab + b² to find 99².
18. 18.If a + b = 11 and ab = 30, what is a² + b²?
19. 19.Use (a + b)(a − b) = a² − b² to find 91 × 89.
20. 20.If a + b = 17 and ab = 70, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 63² − 38².
22. 22.Use (a − b)² = a² − 2ab + b² to find 57².
23. 23.Use a² − b² = (a + b)(a − b) to find 52² − 5².
24. 24.Use (a + b)(a − b) = a² − b² to find 95 × 85.
25. 25.Use (a + b)(a − b) = a² − b² to find 21 × 19.
26. 26.Use (a + b)² = a² + 2ab + b² to find 81².
27. 27.Use (a − b)² = a² − 2ab + b² to find 69².
28. 28.Use (a − b)² = a² − 2ab + b² to find 74².
29. 29.Use (a + b)(a − b) = a² − b² to find 52 × 48.
30. 30.Find the value of x² − 2xy + y² when x = 13 and y = 9.
31. 31.If a + b = 14 and ab = 48, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 72² − 70².
33. 33.If a + b = 6 and ab = 8, what is a² + b²?
34. 34.If a − b = 6 and ab = 72, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 59².
36. 36.Use a² − b² = (a + b)(a − b) to find 30² − 7².
37. 37.If a − b = 1 and ab = 2, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 95².
39. 39.Find the value of x² − y² when x = 12 and y = 2.
40. 40.Use (a + b)(a − b) = a² − b² to find 26 × 14.

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