Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 537 · 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 a² − b² = (a + b)(a − b) to find 34² − 1².
2. 2.Use (a + b)(a − b) = a² − b² to find 46 × 34.
3. 3.Use a² − b² = (a + b)(a − b) to find 32² − 1².
4. 4.If a − b = 2 and ab = 3, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 31².
6. 6.Use (a + b)(a − b) = a² − b² to find 48 × 32.
7. 7.Use (a + b)(a − b) = a² − b² to find 61 × 59.
8. 8.Find the value of x² − 2xy + y² when x = 12 and y = 3.
9. 9.Use (a + b)(a − b) = a² − b² to find 93 × 87.
10. 10.Find the value of x² − y² when x = 7 and y = 6.
11. 11.Use (a + b)(a − b) = a² − b² to find 23 × 17.
12. 12.Find the value of x² − 2xy + y² when x = 7 and y = 5.
13. 13.Use (a + b)² = a² + 2ab + b² to find 39².
14. 14.Use (a + b)² = a² + 2ab + b² to find 54².
15. 15.Use (a − b)² = a² − 2ab + b² to find 48².
16. 16.If a + b = 17 and ab = 72, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 18².
18. 18.Use (a − b)² = a² − 2ab + b² to find 33².
19. 19.Use a² − b² = (a + b)(a − b) to find 32² − 10².
20. 20.Use (a + b)² = a² + 2ab + b² to find 77².
21. 21.Use (a + b)² = a² + 2ab + b² to find 35².
22. 22.Use (a + b)² = a² + 2ab + b² to find 18².
23. 23.Find the value of x² + 2xy + y² when x = 15 and y = 14.
24. 24.Use (a + b)² = a² + 2ab + b² to find 95².
25. 25.Find the value of x² − 2xy + y² when x = 12 and y = 4.
26. 26.Use (a + b)² = a² + 2ab + b² to find 107².
27. 27.Use a² − b² = (a + b)(a − b) to find 90² − 42².
28. 28.Find the value of x² + 2xy + y² when x = 13 and y = 10.
29. 29.Use (a − b)² = a² − 2ab + b² to find 19².
30. 30.Use (a − b)² = a² − 2ab + b² to find 86².
31. 31.Use (a − b)² = a² − 2ab + b² to find 15².
32. 32.Use (a − b)² = a² − 2ab + b² to find 41².
33. 33.Find the value of x² − y² when x = 11 and y = 10.
34. 34.Use a² − b² = (a + b)(a − b) to find 80² − 45².
35. 35.Use a² − b² = (a + b)(a − b) to find 75² − 68².
36. 36.Find the value of x² + 2xy + y² when x = 10 and y = 3.
37. 37.Use (a + b)² = a² + 2ab + b² to find 37².
38. 38.Use (a − b)² = a² − 2ab + b² to find 52².
39. 39.Use (a + b)² = a² + 2ab + b² to find 24².
40. 40.Use (a − b)² = a² − 2ab + b² to find 98².

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