Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 696 · 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 = 4 and y = 3.
2. 2.Find the value of x² − 2xy + y² when x = 10 and y = 2.
3. 3.Use (a − b)² = a² − 2ab + b² to find 41².
4. 4.Find the value of x² + 2xy + y² when x = 14 and y = 13.
5. 5.Use (a + b)² = a² + 2ab + b² to find 87².
6. 6.Find the value of x² − y² when x = 5 and y = 1.
7. 7.Use a² − b² = (a + b)(a − b) to find 24² − 2².
8. 8.If a + b = 13 and ab = 36, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 36² − 4².
10. 10.Use (a + b)² = a² + 2ab + b² to find 66².
11. 11.Find the value of x² − 2xy + y² when x = 9 and y = 7.
12. 12.Find the value of x² − y² when x = 10 and y = 1.
13. 13.Use (a + b)² = a² + 2ab + b² to find 67².
14. 14.If a − b = 7 and ab = 8, what is a² + b²?
15. 15.Use (a + b)(a − b) = a² − b² to find 81 × 79.
16. 16.Use (a + b)² = a² + 2ab + b² to find 25².
17. 17.Use a² − b² = (a + b)(a − b) to find 70² − 52².
18. 18.Use (a + b)(a − b) = a² − b² to find 85 × 75.
19. 19.Use (a + b)(a − b) = a² − b² to find 57 × 43.
20. 20.Use (a + b)² = a² + 2ab + b² to find 97².
21. 21.Use (a − b)² = a² − 2ab + b² to find 99².
22. 22.Find the value of x² − 2xy + y² when x = 11 and y = 2.
23. 23.Use a² − b² = (a + b)(a − b) to find 90² − 42².
24. 24.Find the value of x² − 2xy + y² when x = 14 and y = 10.
25. 25.Use (a + b)(a − b) = a² − b² to find 27 × 13.
26. 26.Use (a − b)² = a² − 2ab + b² to find 34².
27. 27.Use (a + b)² = a² + 2ab + b² to find 21².
28. 28.Use a² − b² = (a + b)(a − b) to find 29² − 18².
29. 29.Use (a + b)(a − b) = a² − b² to find 53 × 47.
30. 30.Use (a − b)² = a² − 2ab + b² to find 27².
31. 31.Use (a + b)² = a² + 2ab + b² to find 14².
32. 32.Find the value of x² − 2xy + y² when x = 9 and y = 2.
33. 33.Use a² − b² = (a + b)(a − b) to find 98² − 84².
34. 34.Use (a + b)² = a² + 2ab + b² to find 61².
35. 35.If a − b = 1 and ab = 2, what is a² + b²?
36. 36.If a + b = 7 and ab = 12, what is a² + b²?
37. 37.If a − b = 7 and ab = 60, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 94 × 86.
39. 39.If a + b = 9 and ab = 18, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 79².

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