Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 932 · 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 86² − 63².
2. 2.Use (a − b)² = a² − 2ab + b² to find 21².
3. 3.Use (a − b)² = a² − 2ab + b² to find 15².
4. 4.Use (a + b)(a − b) = a² − b² to find 43 × 37.
5. 5.Use (a − b)² = a² − 2ab + b² to find 89².
6. 6.Use (a + b)(a − b) = a² − b² to find 101 × 99.
7. 7.Use (a + b)² = a² + 2ab + b² to find 62².
8. 8.Use (a + b)² = a² + 2ab + b² to find 108².
9. 9.If a − b = 2 and ab = 3, what is a² + b²?
10. 10.Find the value of x² + 2xy + y² when x = 12 and y = 5.
11. 11.If a + b = 3 and ab = 2, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 26² − 18².
13. 13.If a + b = 13 and ab = 30, what is a² + b²?
14. 14.Find the value of x² + 2xy + y² when x = 14 and y = 5.
15. 15.Use (a + b)² = a² + 2ab + b² to find 49².
16. 16.Use (a + b)² = a² + 2ab + b² to find 93².
17. 17.Use (a + b)² = a² + 2ab + b² to find 53².
18. 18.Use (a − b)² = a² − 2ab + b² to find 58².
19. 19.Use (a − b)² = a² − 2ab + b² to find 59².
20. 20.Use (a + b)(a − b) = a² − b² to find 58 × 42.
21. 21.Use a² − b² = (a + b)(a − b) to find 92² − 32².
22. 22.Use (a + b)² = a² + 2ab + b² to find 67².
23. 23.Use (a − b)² = a² − 2ab + b² to find 98².
24. 24.If a + b = 14 and ab = 33, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 54².
26. 26.Use (a − b)² = a² − 2ab + b² to find 68².
27. 27.Use a² − b² = (a + b)(a − b) to find 82² − 12².
28. 28.Use (a − b)² = a² − 2ab + b² to find 43².
29. 29.Use (a + b)² = a² + 2ab + b² to find 27².
30. 30.Find the value of x² − y² when x = 9 and y = 4.
31. 31.If a − b = 1 and ab = 110, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 28 × 12.
33. 33.Find the value of x² − 2xy + y² when x = 8 and y = 5.
34. 34.Use (a − b)² = a² − 2ab + b² to find 56².
35. 35.Use (a − b)² = a² − 2ab + b² to find 66².
36. 36.Use a² − b² = (a + b)(a − b) to find 32² − 12².
37. 37.Find the value of x² + 2xy + y² when x = 12 and y = 2.
38. 38.Find the value of x² − y² when x = 7 and y = 1.
39. 39.Use (a + b)(a − b) = a² − b² to find 81 × 79.
40. 40.If a − b = 4 and ab = 5, what is a² + b²?

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