Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 287 · 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 = 9 and y = 5.
2. 2.Find the value of x² + 2xy + y² when x = 13 and y = 2.
3. 3.Use (a + b)(a − b) = a² − b² to find 79 × 61.
4. 4.Find the value of x² − y² when x = 5 and y = 4.
5. 5.Find the value of x² − 2xy + y² when x = 15 and y = 8.
6. 6.Use (a − b)² = a² − 2ab + b² to find 59².
7. 7.Use (a + b)² = a² + 2ab + b² to find 72².
8. 8.If a + b = 11 and ab = 24, what is a² + b²?
9. 9.If a + b = 8 and ab = 15, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 52².
11. 11.Find the value of x² + 2xy + y² when x = 14 and y = 9.
12. 12.Use (a + b)(a − b) = a² − b² to find 24 × 16.
13. 13.If a − b = 1 and ab = 2, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 92² − 54².
15. 15.Use a² − b² = (a + b)(a − b) to find 71² − 44².
16. 16.Use (a − b)² = a² − 2ab + b² to find 65².
17. 17.Find the value of x² + 2xy + y² when x = 10 and y = 4.
18. 18.If a − b = 1 and ab = 6, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 90² − 54².
20. 20.Find the value of x² − 2xy + y² when x = 11 and y = 2.
21. 21.Use (a + b)(a − b) = a² − b² to find 99 × 81.
22. 22.Use (a + b)(a − b) = a² − b² to find 101 × 99.
23. 23.Use (a + b)² = a² + 2ab + b² to find 44².
24. 24.Use (a + b)² = a² + 2ab + b² to find 102².
25. 25.Use a² − b² = (a + b)(a − b) to find 52² − 29².
26. 26.Use (a − b)² = a² − 2ab + b² to find 32².
27. 27.Use (a − b)² = a² − 2ab + b² to find 75².
28. 28.If a + b = 13 and ab = 42, what is a² + b²?
29. 29.If a + b = 14 and ab = 24, what is a² + b²?
30. 30.If a − b = 6 and ab = 72, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 63² − 33².
32. 32.Use a² − b² = (a + b)(a − b) to find 33² − 11².
33. 33.Use (a + b)² = a² + 2ab + b² to find 89².
34. 34.Use a² − b² = (a + b)(a − b) to find 83² − 2².
35. 35.Use a² − b² = (a + b)(a − b) to find 49² − 17².
36. 36.Find the value of x² − 2xy + y² when x = 12 and y = 4.
37. 37.Use (a + b)(a − b) = a² − b² to find 32 × 28.
38. 38.Find the value of x² − 2xy + y² when x = 12 and y = 1.
39. 39.Use a² − b² = (a + b)(a − b) to find 86² − 75².
40. 40.If a + b = 5 and ab = 6, what is a² + b²?

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