Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 296 · 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 35².
2. 2.Use (a + b)(a − b) = a² − b² to find 96 × 84.
3. 3.Use (a − b)² = a² − 2ab + b² to find 87².
4. 4.Use (a + b)² = a² + 2ab + b² to find 74².
5. 5.Use a² − b² = (a + b)(a − b) to find 20² − 16².
6. 6.Use (a + b)² = a² + 2ab + b² to find 108².
7. 7.Use (a + b)(a − b) = a² − b² to find 108 × 92.
8. 8.Use (a + b)(a − b) = a² − b² to find 103 × 97.
9. 9.Use (a + b)(a − b) = a² − b² to find 51 × 49.
10. 10.Use (a + b)² = a² + 2ab + b² to find 18².
11. 11.If a + b = 12 and ab = 32, what is a² + b²?
12. 12.Find the value of x² + 2xy + y² when x = 4 and y = 2.
13. 13.Find the value of x² + 2xy + y² when x = 3 and y = 2.
14. 14.Use a² − b² = (a + b)(a − b) to find 90² − 36².
15. 15.Use (a − b)² = a² − 2ab + b² to find 81².
16. 16.Use (a + b)(a − b) = a² − b² to find 63 × 57.
17. 17.Use (a − b)² = a² − 2ab + b² to find 26².
18. 18.Use (a − b)² = a² − 2ab + b² to find 18².
19. 19.Use a² − b² = (a + b)(a − b) to find 82² − 66².
20. 20.If a + b = 14 and ab = 40, what is a² + b²?
21. 21.Use (a + b)² = a² + 2ab + b² to find 59².
22. 22.Use (a + b)² = a² + 2ab + b² to find 79².
23. 23.If a − b = 4 and ab = 21, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 66².
25. 25.Use (a + b)² = a² + 2ab + b² to find 32².
26. 26.Use a² − b² = (a + b)(a − b) to find 41² − 38².
27. 27.Use (a + b)² = a² + 2ab + b² to find 37².
28. 28.Use (a − b)² = a² − 2ab + b² to find 61².
29. 29.Use (a + b)² = a² + 2ab + b² to find 29².
30. 30.If a − b = 1 and ab = 2, what is a² + b²?
31. 31.Use (a − b)² = a² − 2ab + b² to find 74².
32. 32.Use (a − b)² = a² − 2ab + b² to find 42².
33. 33.Use a² − b² = (a + b)(a − b) to find 52² − 49².
34. 34.Use (a + b)(a − b) = a² − b² to find 73 × 67.
35. 35.Use a² − b² = (a + b)(a − b) to find 74² − 46².
36. 36.Use (a + b)(a − b) = a² − b² to find 107 × 93.
37. 37.Use (a − b)² = a² − 2ab + b² to find 85².
38. 38.Use (a + b)² = a² + 2ab + b² to find 85².
39. 39.Find the value of x² − y² when x = 9 and y = 4.
40. 40.If a − b = 3 and ab = 10, what is a² + b²?

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