Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 307 · 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 28 × 12.
2. 2.Find the value of x² − 2xy + y² when x = 7 and y = 2.
3. 3.Use (a + b)(a − b) = a² − b² to find 102 × 98.
4. 4.Use a² − b² = (a + b)(a − b) to find 45² − 14².
5. 5.Use (a − b)² = a² − 2ab + b² to find 69².
6. 6.Use (a + b)(a − b) = a² − b² to find 104 × 96.
7. 7.Use (a + b)(a − b) = a² − b² to find 108 × 92.
8. 8.Use (a + b)(a − b) = a² − b² to find 66 × 54.
9. 9.Use (a − b)² = a² − 2ab + b² to find 99².
10. 10.If a + b = 4 and ab = 3, what is a² + b²?
11. 11.If a + b = 18 and ab = 80, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 57² − 10².
13. 13.Use a² − b² = (a + b)(a − b) to find 23² − 8².
14. 14.Find the value of x² + 2xy + y² when x = 9 and y = 6.
15. 15.Find the value of x² + 2xy + y² when x = 9 and y = 4.
16. 16.If a − b = 3 and ab = 4, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 103².
18. 18.Use a² − b² = (a + b)(a − b) to find 87² − 19².
19. 19.If a + b = 8 and ab = 15, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 99 × 81.
21. 21.Use (a + b)² = a² + 2ab + b² to find 57².
22. 22.Use (a + b)² = a² + 2ab + b² to find 18².
23. 23.Use (a + b)(a − b) = a² − b² to find 52 × 48.
24. 24.Use (a + b)(a − b) = a² − b² to find 73 × 67.
25. 25.Use a² − b² = (a + b)(a − b) to find 94² − 19².
26. 26.Find the value of x² − 2xy + y² when x = 10 and y = 3.
27. 27.Find the value of x² + 2xy + y² when x = 15 and y = 6.
28. 28.Use (a + b)(a − b) = a² − b² to find 83 × 77.
29. 29.Use (a + b)² = a² + 2ab + b² to find 94².
30. 30.Use (a + b)(a − b) = a² − b² to find 21 × 19.
31. 31.Use (a + b)(a − b) = a² − b² to find 35 × 25.
32. 32.Use (a − b)² = a² − 2ab + b² to find 33².
33. 33.Use (a − b)² = a² − 2ab + b² to find 51².
34. 34.Use a² − b² = (a + b)(a − b) to find 22² − 6².
35. 35.Use (a + b)² = a² + 2ab + b² to find 16².
36. 36.Use (a + b)(a − b) = a² − b² to find 33 × 27.
37. 37.If a − b = 5 and ab = 6, what is a² + b²?
38. 38.Use a² − b² = (a + b)(a − b) to find 30² − 7².
39. 39.Use (a + b)² = a² + 2ab + b² to find 78².
40. 40.Use (a − b)² = a² − 2ab + b² to find 23².

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