Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 319 · 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 59 × 41.
2. 2.Use (a + b)² = a² + 2ab + b² to find 85².
3. 3.Use a² − b² = (a + b)(a − b) to find 76² − 14².
4. 4.Use (a + b)(a − b) = a² − b² to find 42 × 38.
5. 5.Use (a + b)² = a² + 2ab + b² to find 56².
6. 6.Use (a − b)² = a² − 2ab + b² to find 19².
7. 7.Use (a − b)² = a² − 2ab + b² to find 34².
8. 8.Use (a + b)² = a² + 2ab + b² to find 91².
9. 9.If a − b = 8 and ab = 20, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 91² − 75².
11. 11.Find the value of x² + 2xy + y² when x = 7 and y = 3.
12. 12.Use (a − b)² = a² − 2ab + b² to find 57².
13. 13.Use a² − b² = (a + b)(a − b) to find 45² − 14².
14. 14.If a − b = 3 and ab = 18, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 92².
16. 16.If a + b = 9 and ab = 14, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 31².
18. 18.Use a² − b² = (a + b)(a − b) to find 41² − 2².
19. 19.Use (a + b)² = a² + 2ab + b² to find 78².
20. 20.Use (a − b)² = a² − 2ab + b² to find 41².
21. 21.If a + b = 13 and ab = 12, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 42² − 10².
23. 23.Use a² − b² = (a + b)(a − b) to find 70² − 2².
24. 24.Find the value of x² − y² when x = 15 and y = 2.
25. 25.Use a² − b² = (a + b)(a − b) to find 94² − 9².
26. 26.Use a² − b² = (a + b)(a − b) to find 52² − 41².
27. 27.Use (a + b)² = a² + 2ab + b² to find 12².
28. 28.Use (a − b)² = a² − 2ab + b² to find 18².
29. 29.Use (a + b)(a − b) = a² − b² to find 67 × 53.
30. 30.Use a² − b² = (a + b)(a − b) to find 85² − 36².
31. 31.Find the value of x² + 2xy + y² when x = 9 and y = 1.
32. 32.Use (a − b)² = a² − 2ab + b² to find 74².
33. 33.Find the value of x² + 2xy + y² when x = 10 and y = 5.
34. 34.Find the value of x² + 2xy + y² when x = 7 and y = 6.
35. 35.Use (a − b)² = a² − 2ab + b² to find 11².
36. 36.Find the value of x² − y² when x = 13 and y = 7.
37. 37.Use (a + b)² = a² + 2ab + b² to find 13².
38. 38.Find the value of x² − y² when x = 14 and y = 11.
39. 39.Use (a + b)² = a² + 2ab + b² to find 92².
40. 40.Use (a + b)² = a² + 2ab + b² to find 25².

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