Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 468 · 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 31 × 29.
2. 2.Use (a − b)² = a² − 2ab + b² to find 13².
3. 3.Find the value of x² + 2xy + y² when x = 11 and y = 2.
4. 4.Use (a + b)² = a² + 2ab + b² to find 45².
5. 5.Use (a + b)² = a² + 2ab + b² to find 84².
6. 6.Find the value of x² + 2xy + y² when x = 4 and y = 3.
7. 7.Use (a − b)² = a² − 2ab + b² to find 39².
8. 8.Use (a + b)² = a² + 2ab + b² to find 36².
9. 9.If a − b = 1 and ab = 42, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 46².
11. 11.Use (a − b)² = a² − 2ab + b² to find 28².
12. 12.If a − b = 3 and ab = 4, what is a² + b²?
13. 13.If a + b = 3 and ab = 2, what is a² + b²?
14. 14.Find the value of x² − 2xy + y² when x = 9 and y = 5.
15. 15.Find the value of x² + 2xy + y² when x = 6 and y = 1.
16. 16.Use (a + b)² = a² + 2ab + b² to find 29².
17. 17.Use a² − b² = (a + b)(a − b) to find 37² − 10².
18. 18.Find the value of x² − y² when x = 8 and y = 4.
19. 19.Use (a − b)² = a² − 2ab + b² to find 21².
20. 20.Find the value of x² − y² when x = 8 and y = 5.
21. 21.Use a² − b² = (a + b)(a − b) to find 88² − 16².
22. 22.Use a² − b² = (a + b)(a − b) to find 52² − 3².
23. 23.Find the value of x² − 2xy + y² when x = 15 and y = 2.
24. 24.Use a² − b² = (a + b)(a − b) to find 76² − 54².
25. 25.Use (a + b)² = a² + 2ab + b² to find 74².
26. 26.Use (a − b)² = a² − 2ab + b² to find 84².
27. 27.If a + b = 11 and ab = 10, what is a² + b²?
28. 28.If a − b = 5 and ab = 6, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 56².
30. 30.Use (a + b)² = a² + 2ab + b² to find 13².
31. 31.If a + b = 20 and ab = 96, what is a² + b²?
32. 32.Find the value of x² − y² when x = 9 and y = 3.
33. 33.Use (a + b)(a − b) = a² − b² to find 28 × 12.
34. 34.Use (a + b)² = a² + 2ab + b² to find 31².
35. 35.Use (a − b)² = a² − 2ab + b² to find 43².
36. 36.Use (a + b)² = a² + 2ab + b² to find 32².
37. 37.Use (a + b)² = a² + 2ab + b² to find 51².
38. 38.Use (a − b)² = a² − 2ab + b² to find 71².
39. 39.Use (a + b)(a − b) = a² − b² to find 68 × 52.
40. 40.Use a² − b² = (a + b)(a − b) to find 27² − 14².

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