Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 119 · 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 − y² when x = 15 and y = 13.
2. 2.Use a² − b² = (a + b)(a − b) to find 88² − 15².
3. 3.Use (a + b)² = a² + 2ab + b² to find 22².
4. 4.Find the value of x² + 2xy + y² when x = 5 and y = 1.
5. 5.Use (a + b)² = a² + 2ab + b² to find 44².
6. 6.If a − b = 3 and ab = 54, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 43² − 31².
8. 8.Find the value of x² + 2xy + y² when x = 7 and y = 5.
9. 9.Use (a − b)² = a² − 2ab + b² to find 15².
10. 10.Use (a + b)(a − b) = a² − b² to find 27 × 13.
11. 11.Use (a + b)² = a² + 2ab + b² to find 75².
12. 12.Use (a − b)² = a² − 2ab + b² to find 37².
13. 13.Use (a − b)² = a² − 2ab + b² to find 12².
14. 14.If a + b = 16 and ab = 60, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 69².
16. 16.Use (a + b)² = a² + 2ab + b² to find 107².
17. 17.Use (a + b)(a − b) = a² − b² to find 77 × 63.
18. 18.Use (a − b)² = a² − 2ab + b² to find 62².
19. 19.Find the value of x² + 2xy + y² when x = 3 and y = 2.
20. 20.Use (a + b)² = a² + 2ab + b² to find 12².
21. 21.Use (a + b)(a − b) = a² − b² to find 37 × 23.
22. 22.If a + b = 4 and ab = 3, what is a² + b²?
23. 23.Find the value of x² − y² when x = 10 and y = 3.
24. 24.If a + b = 10 and ab = 16, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 69² − 44².
26. 26.Use (a − b)² = a² − 2ab + b² to find 82².
27. 27.Find the value of x² − y² when x = 13 and y = 8.
28. 28.Use (a − b)² = a² − 2ab + b² to find 94².
29. 29.Use (a − b)² = a² − 2ab + b² to find 19².
30. 30.Use (a + b)² = a² + 2ab + b² to find 29².
31. 31.Use (a − b)² = a² − 2ab + b² to find 88².
32. 32.If a + b = 10 and ab = 21, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 22 × 18.
34. 34.Use (a + b)² = a² + 2ab + b² to find 21².
35. 35.Use (a + b)² = a² + 2ab + b² to find 53².
36. 36.Use (a − b)² = a² − 2ab + b² to find 63².
37. 37.Use (a + b)(a − b) = a² − b² to find 21 × 19.
38. 38.Use a² − b² = (a + b)(a − b) to find 50² − 39².
39. 39.Use (a + b)² = a² + 2ab + b² to find 34².
40. 40.If a − b = 2 and ab = 3, what is a² + b²?

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