Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 472 · 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 56 × 44.
2. 2.If a + b = 12 and ab = 27, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 66².
4. 4.Use a² − b² = (a + b)(a − b) to find 23² − 13².
5. 5.Use a² − b² = (a + b)(a − b) to find 66² − 5².
6. 6.Find the value of x² + 2xy + y² when x = 12 and y = 5.
7. 7.Use (a + b)² = a² + 2ab + b² to find 74².
8. 8.Use a² − b² = (a + b)(a − b) to find 66² − 23².
9. 9.If a − b = 2 and ab = 80, what is a² + b²?
10. 10.If a + b = 3 and ab = 2, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 77².
12. 12.Use (a + b)² = a² + 2ab + b² to find 18².
13. 13.Use (a + b)² = a² + 2ab + b² to find 59².
14. 14.Use (a − b)² = a² − 2ab + b² to find 21².
15. 15.Find the value of x² − 2xy + y² when x = 11 and y = 1.
16. 16.Use a² − b² = (a + b)(a − b) to find 30² − 20².
17. 17.Use (a + b)(a − b) = a² − b² to find 79 × 61.
18. 18.If a + b = 17 and ab = 60, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 12².
20. 20.If a − b = 1 and ab = 90, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 84² − 24².
22. 22.Find the value of x² + 2xy + y² when x = 7 and y = 3.
23. 23.Find the value of x² − 2xy + y² when x = 3 and y = 1.
24. 24.Find the value of x² − 2xy + y² when x = 11 and y = 2.
25. 25.Use (a − b)² = a² − 2ab + b² to find 67².
26. 26.Use (a − b)² = a² − 2ab + b² to find 38².
27. 27.Use (a + b)² = a² + 2ab + b² to find 61².
28. 28.Find the value of x² + 2xy + y² when x = 3 and y = 1.
29. 29.Use (a − b)² = a² − 2ab + b² to find 45².
30. 30.Use a² − b² = (a + b)(a − b) to find 26² − 12².
31. 31.Use a² − b² = (a + b)(a − b) to find 50² − 41².
32. 32.Use (a + b)(a − b) = a² − b² to find 81 × 79.
33. 33.Use (a − b)² = a² − 2ab + b² to find 17².
34. 34.Use (a + b)² = a² + 2ab + b² to find 54².
35. 35.If a + b = 17 and ab = 70, what is a² + b²?
36. 36.If a − b = 5 and ab = 24, what is a² + b²?
37. 37.If a − b = 3 and ab = 10, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 41 × 39.
39. 39.Use (a − b)² = a² − 2ab + b² to find 95².
40. 40.Use (a + b)² = a² + 2ab + b² to find 87².

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