Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 473 · 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 33 × 27.
2. 2.Use (a + b)² = a² + 2ab + b² to find 37².
3. 3.Use (a + b)² = a² + 2ab + b² to find 24².
4. 4.Use (a + b)(a − b) = a² − b² to find 24 × 16.
5. 5.Use (a + b)(a − b) = a² − b² to find 27 × 13.
6. 6.Find the value of x² − 2xy + y² when x = 6 and y = 5.
7. 7.Use (a − b)² = a² − 2ab + b² to find 19².
8. 8.Use (a + b)(a − b) = a² − b² to find 87 × 73.
9. 9.Use (a − b)² = a² − 2ab + b² to find 63².
10. 10.Use (a + b)(a − b) = a² − b² to find 102 × 98.
11. 11.Use a² − b² = (a + b)(a − b) to find 94² − 59².
12. 12.Use (a + b)(a − b) = a² − b² to find 92 × 88.
13. 13.Use (a + b)(a − b) = a² − b² to find 71 × 69.
14. 14.Use (a + b)² = a² + 2ab + b² to find 29².
15. 15.If a + b = 17 and ab = 70, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 36 × 24.
17. 17.Use a² − b² = (a + b)(a − b) to find 62² − 1².
18. 18.If a + b = 3 and ab = 2, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 89².
20. 20.Use (a − b)² = a² − 2ab + b² to find 15².
21. 21.Use (a + b)² = a² + 2ab + b² to find 13².
22. 22.Use (a + b)² = a² + 2ab + b² to find 56².
23. 23.Use (a − b)² = a² − 2ab + b² to find 28².
24. 24.Use (a + b)² = a² + 2ab + b² to find 91².
25. 25.Use (a + b)(a − b) = a² − b² to find 56 × 44.
26. 26.Use (a + b)(a − b) = a² − b² to find 91 × 89.
27. 27.Use (a + b)² = a² + 2ab + b² to find 49².
28. 28.Use (a + b)² = a² + 2ab + b² to find 22².
29. 29.Use (a + b)² = a² + 2ab + b² to find 33².
30. 30.Find the value of x² − 2xy + y² when x = 4 and y = 2.
31. 31.Use (a + b)(a − b) = a² − b² to find 26 × 14.
32. 32.If a + b = 10 and ab = 24, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 86² − 54².
34. 34.Use (a − b)² = a² − 2ab + b² to find 54².
35. 35.Use (a + b)² = a² + 2ab + b² to find 108².
36. 36.Use a² − b² = (a + b)(a − b) to find 20² − 1².
37. 37.If a − b = 4 and ab = 21, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 17².
39. 39.Use (a + b)(a − b) = a² − b² to find 108 × 92.
40. 40.Use a² − b² = (a + b)(a − b) to find 41² − 14².

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