Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 732 · 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 47² − 33².
2. 2.Use (a + b)² = a² + 2ab + b² to find 65².
3. 3.If a + b = 3 and ab = 2, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 37².
5. 5.Use (a + b)² = a² + 2ab + b² to find 95².
6. 6.Use (a − b)² = a² − 2ab + b² to find 26².
7. 7.Use (a + b)² = a² + 2ab + b² to find 38².
8. 8.Use a² − b² = (a + b)(a − b) to find 39² − 8².
9. 9.If a − b = 3 and ab = 4, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 19².
11. 11.Use (a + b)² = a² + 2ab + b² to find 93².
12. 12.Use (a − b)² = a² − 2ab + b² to find 46².
13. 13.Use (a + b)(a − b) = a² − b² to find 79 × 61.
14. 14.Use (a + b)(a − b) = a² − b² to find 56 × 44.
15. 15.Use a² − b² = (a + b)(a − b) to find 33² − 31².
16. 16.Find the value of x² − y² when x = 8 and y = 1.
17. 17.Find the value of x² − 2xy + y² when x = 10 and y = 2.
18. 18.If a + b = 14 and ab = 40, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 13².
20. 20.Use (a − b)² = a² − 2ab + b² to find 41².
21. 21.If a + b = 7 and ab = 12, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 49².
23. 23.Find the value of x² − y² when x = 8 and y = 2.
24. 24.If a + b = 8 and ab = 7, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 95².
26. 26.Use (a + b)² = a² + 2ab + b² to find 109².
27. 27.Use (a + b)² = a² + 2ab + b² to find 88².
28. 28.Use (a + b)² = a² + 2ab + b² to find 18².
29. 29.If a + b = 22 and ab = 120, what is a² + b²?
30. 30.Use (a + b)(a − b) = a² − b² to find 75 × 65.
31. 31.Find the value of x² − 2xy + y² when x = 14 and y = 9.
32. 32.Use (a + b)(a − b) = a² − b² to find 33 × 27.
33. 33.Use (a + b)² = a² + 2ab + b² to find 87².
34. 34.Use (a + b)(a − b) = a² − b² to find 71 × 69.
35. 35.Use (a + b)(a − b) = a² − b² to find 51 × 49.
36. 36.Use a² − b² = (a + b)(a − b) to find 91² − 71².
37. 37.Use (a + b)(a − b) = a² − b² to find 25 × 15.
38. 38.Use (a − b)² = a² − 2ab + b² to find 98².
39. 39.Find the value of x² − y² when x = 3 and y = 2.
40. 40.Use a² − b² = (a + b)(a − b) to find 28² − 26².

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