Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 42 · 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.Find the value of x² − 2xy + y² when x = 10 and y = 4.
2. 2.Use (a − b)² = a² − 2ab + b² to find 85².
3. 3.If a − b = 9 and ab = 22, what is a² + b²?
4. 4.If a − b = 5 and ab = 66, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 93² − 2².
6. 6.Use (a − b)² = a² − 2ab + b² to find 12².
7. 7.Use (a + b)² = a² + 2ab + b² to find 81².
8. 8.Use a² − b² = (a + b)(a − b) to find 23² − 22².
9. 9.Use a² − b² = (a + b)(a − b) to find 84² − 16².
10. 10.Use (a + b)(a − b) = a² − b² to find 28 × 12.
11. 11.If a + b = 11 and ab = 10, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 81² − 33².
13. 13.Use (a − b)² = a² − 2ab + b² to find 95².
14. 14.Use (a − b)² = a² − 2ab + b² to find 77².
15. 15.Use (a + b)² = a² + 2ab + b² to find 23².
16. 16.Use (a + b)(a − b) = a² − b² to find 47 × 33.
17. 17.Use a² − b² = (a + b)(a − b) to find 83² − 75².
18. 18.Use (a − b)² = a² − 2ab + b² to find 43².
19. 19.Use (a − b)² = a² − 2ab + b² to find 25².
20. 20.Use (a − b)² = a² − 2ab + b² to find 38².
21. 21.Use (a + b)(a − b) = a² − b² to find 31 × 29.
22. 22.Use (a + b)² = a² + 2ab + b² to find 77².
23. 23.Use (a + b)(a − b) = a² − b² to find 29 × 11.
24. 24.Use (a + b)(a − b) = a² − b² to find 99 × 81.
25. 25.Use (a − b)² = a² − 2ab + b² to find 27².
26. 26.Use (a − b)² = a² − 2ab + b² to find 37².
27. 27.If a + b = 17 and ab = 70, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 71² − 59².
29. 29.If a + b = 7 and ab = 12, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 38².
31. 31.Use (a + b)(a − b) = a² − b² to find 33 × 27.
32. 32.Use a² − b² = (a + b)(a − b) to find 66² − 65².
33. 33.Use a² − b² = (a + b)(a − b) to find 29² − 23².
34. 34.Use (a + b)² = a² + 2ab + b² to find 21².
35. 35.If a − b = 3 and ab = 4, what is a² + b²?
36. 36.Find the value of x² − 2xy + y² when x = 14 and y = 4.
37. 37.Use (a − b)² = a² − 2ab + b² to find 14².
38. 38.Use (a + b)² = a² + 2ab + b² to find 32².
39. 39.Use (a + b)(a − b) = a² − b² to find 105 × 95.
40. 40.Find the value of x² + 2xy + y² when x = 3 and y = 1.

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