Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 824 · 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 105 × 95.
2. 2.Use (a − b)² = a² − 2ab + b² to find 13².
3. 3.Use (a + b)² = a² + 2ab + b² to find 58².
4. 4.If a + b = 7 and ab = 12, what is a² + b²?
5. 5.If a + b = 16 and ab = 63, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 62² − 43².
7. 7.Use (a + b)² = a² + 2ab + b² to find 99².
8. 8.Use (a + b)(a − b) = a² − b² to find 94 × 86.
9. 9.Find the value of x² − y² when x = 10 and y = 4.
10. 10.If a − b = 3 and ab = 18, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 27² − 7².
12. 12.Use (a + b)(a − b) = a² − b² to find 36 × 24.
13. 13.If a + b = 5 and ab = 6, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 109 × 91.
15. 15.If a + b = 8 and ab = 12, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 88².
17. 17.Find the value of x² + 2xy + y² when x = 6 and y = 1.
18. 18.Use (a + b)(a − b) = a² − b² to find 75 × 65.
19. 19.Use a² − b² = (a + b)(a − b) to find 39² − 29².
20. 20.Find the value of x² + 2xy + y² when x = 5 and y = 2.
21. 21.Use (a − b)² = a² − 2ab + b² to find 59².
22. 22.Use (a + b)² = a² + 2ab + b² to find 55².
23. 23.Use (a + b)² = a² + 2ab + b² to find 12².
24. 24.Use (a + b)² = a² + 2ab + b² to find 33².
25. 25.Use (a − b)² = a² − 2ab + b² to find 18².
26. 26.Use a² − b² = (a + b)(a − b) to find 63² − 53².
27. 27.Use (a + b)² = a² + 2ab + b² to find 24².
28. 28.Use (a − b)² = a² − 2ab + b² to find 19².
29. 29.Use a² − b² = (a + b)(a − b) to find 78² − 34².
30. 30.Use (a + b)(a − b) = a² − b² to find 79 × 61.
31. 31.Use (a + b)² = a² + 2ab + b² to find 87².
32. 32.Use (a + b)(a − b) = a² − b² to find 93 × 87.
33. 33.Use a² − b² = (a + b)(a − b) to find 37² − 25².
34. 34.If a + b = 3 and ab = 2, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 66².
36. 36.Use a² − b² = (a + b)(a − b) to find 41² − 10².
37. 37.Use (a − b)² = a² − 2ab + b² to find 34².
38. 38.Use (a + b)² = a² + 2ab + b² to find 101².
39. 39.If a − b = 5 and ab = 14, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 96².

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