Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 990 · 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 98².
2. 2.Use (a − b)² = a² − 2ab + b² to find 14².
3. 3.Use (a + b)² = a² + 2ab + b² to find 22².
4. 4.Use (a + b)² = a² + 2ab + b² to find 33².
5. 5.If a + b = 16 and ab = 60, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 72 × 68.
7. 7.Find the value of x² + 2xy + y² when x = 8 and y = 5.
8. 8.If a + b = 6 and ab = 8, what is a² + b²?
9. 9.Use (a − b)² = a² − 2ab + b² to find 49².
10. 10.Use a² − b² = (a + b)(a − b) to find 88² − 4².
11. 11.Use a² − b² = (a + b)(a − b) to find 22² − 6².
12. 12.Use (a − b)² = a² − 2ab + b² to find 28².
13. 13.If a + b = 14 and ab = 45, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 18².
15. 15.Use (a − b)² = a² − 2ab + b² to find 89².
16. 16.Find the value of x² − 2xy + y² when x = 5 and y = 4.
17. 17.Use (a − b)² = a² − 2ab + b² to find 82².
18. 18.Find the value of x² − 2xy + y² when x = 9 and y = 8.
19. 19.Use (a + b)(a − b) = a² − b² to find 26 × 14.
20. 20.Use (a − b)² = a² − 2ab + b² to find 55².
21. 21.Use (a − b)² = a² − 2ab + b² to find 45².
22. 22.Use (a + b)² = a² + 2ab + b² to find 29².
23. 23.Use (a − b)² = a² − 2ab + b² to find 48².
24. 24.If a + b = 20 and ab = 99, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 62² − 57².
26. 26.Use (a − b)² = a² − 2ab + b² to find 67².
27. 27.Use (a − b)² = a² − 2ab + b² to find 85².
28. 28.Use (a + b)² = a² + 2ab + b² to find 25².
29. 29.If a − b = 3 and ab = 10, what is a² + b²?
30. 30.If a + b = 13 and ab = 30, what is a² + b²?
31. 31.If a + b = 7 and ab = 6, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 55² − 3².
33. 33.Use a² − b² = (a + b)(a − b) to find 54² − 10².
34. 34.Use (a + b)² = a² + 2ab + b² to find 56².
35. 35.Use (a − b)² = a² − 2ab + b² to find 74².
36. 36.Use a² − b² = (a + b)(a − b) to find 59² − 9².
37. 37.Find the value of x² − y² when x = 14 and y = 5.
38. 38.Use a² − b² = (a + b)(a − b) to find 31² − 21².
39. 39.Find the value of x² − 2xy + y² when x = 15 and y = 5.
40. 40.Use (a + b)² = a² + 2ab + b² to find 23².

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