Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 656 · 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 80² − 52².
2. 2.Use (a + b)(a − b) = a² − b² to find 77 × 63.
3. 3.Use (a − b)² = a² − 2ab + b² to find 49².
4. 4.Use a² − b² = (a + b)(a − b) to find 91² − 25².
5. 5.Use (a − b)² = a² − 2ab + b² to find 75².
6. 6.Use a² − b² = (a + b)(a − b) to find 59² − 54².
7. 7.Use (a − b)² = a² − 2ab + b² to find 61².
8. 8.Use (a − b)² = a² − 2ab + b² to find 17².
9. 9.Use (a + b)² = a² + 2ab + b² to find 104².
10. 10.If a − b = 6 and ab = 16, what is a² + b²?
11. 11.Find the value of x² − 2xy + y² when x = 8 and y = 7.
12. 12.Use (a − b)² = a² − 2ab + b² to find 74².
13. 13.Use a² − b² = (a + b)(a − b) to find 37² − 22².
14. 14.Use (a + b)² = a² + 2ab + b² to find 44².
15. 15.Use (a + b)² = a² + 2ab + b² to find 51².
16. 16.Use (a − b)² = a² − 2ab + b² to find 67².
17. 17.Use (a + b)² = a² + 2ab + b² to find 53².
18. 18.Use (a + b)² = a² + 2ab + b² to find 21².
19. 19.If a − b = 4 and ab = 32, what is a² + b²?
20. 20.If a + b = 7 and ab = 6, what is a² + b²?
21. 21.If a − b = 3 and ab = 28, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 18².
23. 23.Use (a − b)² = a² − 2ab + b² to find 37².
24. 24.Use (a − b)² = a² − 2ab + b² to find 21².
25. 25.If a − b = 1 and ab = 2, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 25².
27. 27.If a + b = 3 and ab = 2, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 90² − 18².
29. 29.Use a² − b² = (a + b)(a − b) to find 20² − 9².
30. 30.Use a² − b² = (a + b)(a − b) to find 88² − 21².
31. 31.Use (a − b)² = a² − 2ab + b² to find 41².
32. 32.Use (a + b)² = a² + 2ab + b² to find 101².
33. 33.Use (a + b)² = a² + 2ab + b² to find 46².
34. 34.Use (a + b)² = a² + 2ab + b² to find 94².
35. 35.Find the value of x² + 2xy + y² when x = 9 and y = 7.
36. 36.Use (a − b)² = a² − 2ab + b² to find 24².
37. 37.If a − b = 2 and ab = 3, what is a² + b²?
38. 38.If a + b = 7 and ab = 10, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 81².
40. 40.Use (a + b)² = a² + 2ab + b² to find 14².

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