Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 400 · 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)² = a² + 2ab + b² to find 89².
2. 2.Use (a + b)² = a² + 2ab + b² to find 25².
3. 3.Find the value of x² + 2xy + y² when x = 15 and y = 14.
4. 4.Use (a − b)² = a² − 2ab + b² to find 22².
5. 5.Use a² − b² = (a + b)(a − b) to find 78² − 60².
6. 6.If a + b = 21 and ab = 108, what is a² + b²?
7. 7.Use (a + b)(a − b) = a² − b² to find 96 × 84.
8. 8.Use (a − b)² = a² − 2ab + b² to find 28².
9. 9.Use (a − b)² = a² − 2ab + b² to find 81².
10. 10.Use a² − b² = (a + b)(a − b) to find 41² − 8².
11. 11.Use (a − b)² = a² − 2ab + b² to find 19².
12. 12.Use (a + b)² = a² + 2ab + b² to find 98².
13. 13.Use a² − b² = (a + b)(a − b) to find 81² − 55².
14. 14.Use (a − b)² = a² − 2ab + b² to find 57².
15. 15.Use a² − b² = (a + b)(a − b) to find 32² − 31².
16. 16.If a + b = 12 and ab = 27, what is a² + b²?
17. 17.If a − b = 3 and ab = 54, what is a² + b²?
18. 18.Use (a + b)² = a² + 2ab + b² to find 35².
19. 19.Use (a + b)² = a² + 2ab + b² to find 95².
20. 20.If a + b = 8 and ab = 12, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 63 × 57.
22. 22.Use (a + b)(a − b) = a² − b² to find 33 × 27.
23. 23.Use a² − b² = (a + b)(a − b) to find 47² − 23².
24. 24.Find the value of x² − y² when x = 10 and y = 9.
25. 25.Use (a − b)² = a² − 2ab + b² to find 75².
26. 26.Use a² − b² = (a + b)(a − b) to find 43² − 7².
27. 27.If a + b = 5 and ab = 4, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 42².
29. 29.Use (a + b)² = a² + 2ab + b² to find 53².
30. 30.Use (a − b)² = a² − 2ab + b² to find 15².
31. 31.Use (a − b)² = a² − 2ab + b² to find 29².
32. 32.Use a² − b² = (a + b)(a − b) to find 48² − 26².
33. 33.Use (a + b)(a − b) = a² − b² to find 47 × 33.
34. 34.Use (a + b)² = a² + 2ab + b² to find 67².
35. 35.Use (a + b)² = a² + 2ab + b² to find 79².
36. 36.Use (a + b)² = a² + 2ab + b² to find 18².
37. 37.Use (a + b)² = a² + 2ab + b² to find 54².
38. 38.Use (a + b)² = a² + 2ab + b² to find 91².
39. 39.Use (a + b)(a − b) = a² − b² to find 42 × 38.
40. 40.Use (a + b)(a − b) = a² − b² to find 69 × 51.

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