Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 842 · 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 67².
2. 2.Use a² − b² = (a + b)(a − b) to find 42² − 9².
3. 3.Use (a − b)² = a² − 2ab + b² to find 57².
4. 4.Use a² − b² = (a + b)(a − b) to find 61² − 15².
5. 5.Find the value of x² − y² when x = 3 and y = 1.
6. 6.Use (a + b)² = a² + 2ab + b² to find 28².
7. 7.Use (a + b)² = a² + 2ab + b² to find 97².
8. 8.Find the value of x² − y² when x = 13 and y = 1.
9. 9.Use (a − b)² = a² − 2ab + b² to find 51².
10. 10.Use a² − b² = (a + b)(a − b) to find 93² − 92².
11. 11.Use (a + b)² = a² + 2ab + b² to find 33².
12. 12.Use (a − b)² = a² − 2ab + b² to find 91².
13. 13.Find the value of x² + 2xy + y² when x = 8 and y = 5.
14. 14.Find the value of x² − y² when x = 4 and y = 2.
15. 15.Use (a − b)² = a² − 2ab + b² to find 56².
16. 16.Use (a + b)(a − b) = a² − b² to find 101 × 99.
17. 17.Use (a + b)² = a² + 2ab + b² to find 44².
18. 18.If a + b = 13 and ab = 36, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 18².
20. 20.Use a² − b² = (a + b)(a − b) to find 29² − 9².
21. 21.Use (a − b)² = a² − 2ab + b² to find 74².
22. 22.Use (a + b)² = a² + 2ab + b² to find 48².
23. 23.Use (a + b)(a − b) = a² − b² to find 31 × 29.
24. 24.Use (a + b)(a − b) = a² − b² to find 28 × 12.
25. 25.Use (a + b)² = a² + 2ab + b² to find 79².
26. 26.Use (a − b)² = a² − 2ab + b² to find 35².
27. 27.Use (a + b)² = a² + 2ab + b² to find 36².
28. 28.Use a² − b² = (a + b)(a − b) to find 64² − 2².
29. 29.If a + b = 10 and ab = 24, what is a² + b²?
30. 30.Use (a + b)(a − b) = a² − b² to find 94 × 86.
31. 31.Use (a − b)² = a² − 2ab + b² to find 31².
32. 32.If a − b = 2 and ab = 63, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 105 × 95.
34. 34.Use a² − b² = (a + b)(a − b) to find 28² − 24².
35. 35.Use (a + b)² = a² + 2ab + b² to find 88².
36. 36.If a + b = 7 and ab = 12, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 18².
38. 38.Use (a + b)(a − b) = a² − b² to find 63 × 57.
39. 39.Use a² − b² = (a + b)(a − b) to find 30² − 2².
40. 40.Find the value of x² + 2xy + y² when x = 11 and y = 2.

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