Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 301 · 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 = 14 and y = 3.
2. 2.Find the value of x² − y² when x = 5 and y = 1.
3. 3.Use (a − b)² = a² − 2ab + b² to find 69².
4. 4.Find the value of x² − 2xy + y² when x = 9 and y = 1.
5. 5.Use (a + b)(a − b) = a² − b² to find 44 × 36.
6. 6.Use a² − b² = (a + b)(a − b) to find 92² − 29².
7. 7.Use a² − b² = (a + b)(a − b) to find 72² − 16².
8. 8.If a + b = 6 and ab = 5, what is a² + b²?
9. 9.Use (a + b)(a − b) = a² − b² to find 43 × 37.
10. 10.Use (a − b)² = a² − 2ab + b² to find 66².
11. 11.Use (a + b)² = a² + 2ab + b² to find 35².
12. 12.Use (a + b)² = a² + 2ab + b² to find 57².
13. 13.Use a² − b² = (a + b)(a − b) to find 22² − 1².
14. 14.Use (a − b)² = a² − 2ab + b² to find 97².
15. 15.Use (a + b)² = a² + 2ab + b² to find 54².
16. 16.Use (a − b)² = a² − 2ab + b² to find 31².
17. 17.Use a² − b² = (a + b)(a − b) to find 98² − 50².
18. 18.Use (a + b)² = a² + 2ab + b² to find 44².
19. 19.Use (a + b)² = a² + 2ab + b² to find 59².
20. 20.Use (a + b)(a − b) = a² − b² to find 87 × 73.
21. 21.Find the value of x² + 2xy + y² when x = 11 and y = 4.
22. 22.Use a² − b² = (a + b)(a − b) to find 66² − 56².
23. 23.Use (a + b)(a − b) = a² − b² to find 39 × 21.
24. 24.Use a² − b² = (a + b)(a − b) to find 40² − 2².
25. 25.Find the value of x² + 2xy + y² when x = 6 and y = 2.
26. 26.Use (a − b)² = a² − 2ab + b² to find 68².
27. 27.Use (a + b)(a − b) = a² − b² to find 37 × 23.
28. 28.Use (a + b)² = a² + 2ab + b² to find 108².
29. 29.Use (a + b)² = a² + 2ab + b² to find 83².
30. 30.Use (a − b)² = a² − 2ab + b² to find 81².
31. 31.Use (a + b)² = a² + 2ab + b² to find 65².
32. 32.Find the value of x² − 2xy + y² when x = 4 and y = 2.
33. 33.Use (a − b)² = a² − 2ab + b² to find 61².
34. 34.Use (a + b)² = a² + 2ab + b² to find 63².
35. 35.Use (a + b)² = a² + 2ab + b² to find 74².
36. 36.Use (a + b)² = a² + 2ab + b² to find 62².
37. 37.Use (a − b)² = a² − 2ab + b² to find 83².
38. 38.Use (a − b)² = a² − 2ab + b² to find 49².
39. 39.If a − b = 8 and ab = 9, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 84².

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