Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 368 · 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 65 × 55.
2. 2.Use (a − b)² = a² − 2ab + b² to find 63².
3. 3.Use (a + b)² = a² + 2ab + b² to find 64².
4. 4.Use (a + b)² = a² + 2ab + b² to find 36².
5. 5.Use (a + b)² = a² + 2ab + b² to find 21².
6. 6.Use a² − b² = (a + b)(a − b) to find 71² − 56².
7. 7.Use (a − b)² = a² − 2ab + b² to find 43².
8. 8.Use (a − b)² = a² − 2ab + b² to find 15².
9. 9.Use a² − b² = (a + b)(a − b) to find 44² − 8².
10. 10.Use a² − b² = (a + b)(a − b) to find 24² − 2².
11. 11.If a + b = 8 and ab = 15, what is a² + b²?
12. 12.Use (a + b)(a − b) = a² − b² to find 88 × 72.
13. 13.Use (a − b)² = a² − 2ab + b² to find 82².
14. 14.Use (a − b)² = a² − 2ab + b² to find 92².
15. 15.Use (a − b)² = a² − 2ab + b² to find 42².
16. 16.Use (a − b)² = a² − 2ab + b² to find 81².
17. 17.Use (a + b)(a − b) = a² − b² to find 91 × 89.
18. 18.Use (a − b)² = a² − 2ab + b² to find 68².
19. 19.Find the value of x² + 2xy + y² when x = 3 and y = 1.
20. 20.If a + b = 5 and ab = 4, what is a² + b²?
21. 21.If a − b = 1 and ab = 2, what is a² + b²?
22. 22.Find the value of x² − y² when x = 11 and y = 10.
23. 23.Use (a + b)² = a² + 2ab + b² to find 97².
24. 24.Use (a + b)² = a² + 2ab + b² to find 44².
25. 25.Find the value of x² − y² when x = 7 and y = 3.
26. 26.Use (a + b)(a − b) = a² − b² to find 109 × 91.
27. 27.If a + b = 23 and ab = 132, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 25².
29. 29.Use a² − b² = (a + b)(a − b) to find 36² − 34².
30. 30.Use a² − b² = (a + b)(a − b) to find 70² − 19².
31. 31.Find the value of x² − y² when x = 13 and y = 2.
32. 32.Use (a + b)² = a² + 2ab + b² to find 14².
33. 33.If a − b = 3 and ab = 18, what is a² + b²?
34. 34.If a + b = 9 and ab = 8, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 19².
36. 36.Use (a + b)(a − b) = a² − b² to find 96 × 84.
37. 37.Use (a + b)(a − b) = a² − b² to find 35 × 25.
38. 38.Use (a + b)(a − b) = a² − b² to find 49 × 31.
39. 39.Use (a + b)(a − b) = a² − b² to find 108 × 92.
40. 40.Use a² − b² = (a + b)(a − b) to find 28² − 9².

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