Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 685 · 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 94² − 16².
2. 2.Use (a − b)² = a² − 2ab + b² to find 98².
3. 3.Use (a − b)² = a² − 2ab + b² to find 27².
4. 4.Use a² − b² = (a + b)(a − b) to find 50² − 2².
5. 5.Use (a + b)² = a² + 2ab + b² to find 47².
6. 6.Use a² − b² = (a + b)(a − b) to find 76² − 37².
7. 7.Use (a + b)(a − b) = a² − b² to find 65 × 55.
8. 8.Use (a + b)(a − b) = a² − b² to find 74 × 66.
9. 9.Use (a + b)² = a² + 2ab + b² to find 67².
10. 10.Use a² − b² = (a + b)(a − b) to find 23² − 3².
11. 11.Use (a + b)² = a² + 2ab + b² to find 18².
12. 12.Use a² − b² = (a + b)(a − b) to find 77² − 32².
13. 13.Use (a + b)(a − b) = a² − b² to find 93 × 87.
14. 14.If a + b = 5 and ab = 6, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 49².
16. 16.Use (a − b)² = a² − 2ab + b² to find 44².
17. 17.Use (a − b)² = a² − 2ab + b² to find 67².
18. 18.Use (a + b)(a − b) = a² − b² to find 85 × 75.
19. 19.Use (a − b)² = a² − 2ab + b² to find 38².
20. 20.Use (a − b)² = a² − 2ab + b² to find 83².
21. 21.Use (a + b)² = a² + 2ab + b² to find 11².
22. 22.Find the value of x² + 2xy + y² when x = 10 and y = 5.
23. 23.Use (a + b)(a − b) = a² − b² to find 61 × 59.
24. 24.Use (a + b)² = a² + 2ab + b² to find 75².
25. 25.Use (a + b)² = a² + 2ab + b² to find 55².
26. 26.Use (a + b)² = a² + 2ab + b² to find 56².
27. 27.If a − b = 4 and ab = 45, what is a² + b²?
28. 28.Find the value of x² + 2xy + y² when x = 8 and y = 7.
29. 29.Use (a − b)² = a² − 2ab + b² to find 65².
30. 30.If a + b = 8 and ab = 15, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 59².
32. 32.Use (a − b)² = a² − 2ab + b² to find 17².
33. 33.Use (a + b)(a − b) = a² − b² to find 25 × 15.
34. 34.Use a² − b² = (a + b)(a − b) to find 67² − 17².
35. 35.Use (a − b)² = a² − 2ab + b² to find 68².
36. 36.Find the value of x² − y² when x = 13 and y = 10.
37. 37.Use (a + b)(a − b) = a² − b² to find 29 × 11.
38. 38.Use (a + b)(a − b) = a² − b² to find 107 × 93.
39. 39.If a + b = 11 and ab = 24, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 64² − 43².

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