Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 358 · 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 = 3 and y = 2.
2. 2.Find the value of x² − 2xy + y² when x = 6 and y = 2.
3. 3.If a − b = 1 and ab = 2, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 67².
5. 5.If a + b = 9 and ab = 8, what is a² + b²?
6. 6.Find the value of x² − 2xy + y² when x = 5 and y = 3.
7. 7.Use a² − b² = (a + b)(a − b) to find 78² − 39².
8. 8.Find the value of x² + 2xy + y² when x = 5 and y = 2.
9. 9.If a + b = 12 and ab = 32, what is a² + b²?
10. 10.Find the value of x² + 2xy + y² when x = 14 and y = 10.
11. 11.Use (a + b)(a − b) = a² − b² to find 43 × 37.
12. 12.If a + b = 14 and ab = 33, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 78².
14. 14.If a − b = 2 and ab = 24, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 22² − 12².
16. 16.Find the value of x² − y² when x = 15 and y = 4.
17. 17.Use (a + b)(a − b) = a² − b² to find 68 × 52.
18. 18.If a − b = 1 and ab = 12, what is a² + b²?
19. 19.If a − b = 3 and ab = 108, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 93 × 87.
21. 21.If a − b = 1 and ab = 110, what is a² + b²?
22. 22.Find the value of x² + 2xy + y² when x = 11 and y = 3.
23. 23.If a + b = 3 and ab = 2, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 92 × 88.
25. 25.Use (a + b)² = a² + 2ab + b² to find 81².
26. 26.Find the value of x² + 2xy + y² when x = 3 and y = 2.
27. 27.Use (a − b)² = a² − 2ab + b² to find 52².
28. 28.Use (a + b)² = a² + 2ab + b² to find 48².
29. 29.Use (a + b)(a − b) = a² − b² to find 39 × 21.
30. 30.Use (a − b)² = a² − 2ab + b² to find 58².
31. 31.Use a² − b² = (a + b)(a − b) to find 24² − 17².
32. 32.Use (a − b)² = a² − 2ab + b² to find 18².
33. 33.Use (a − b)² = a² − 2ab + b² to find 45².
34. 34.Find the value of x² + 2xy + y² when x = 4 and y = 3.
35. 35.Use (a − b)² = a² − 2ab + b² to find 38².
36. 36.Use (a + b)(a − b) = a² − b² to find 104 × 96.
37. 37.Use (a + b)² = a² + 2ab + b² to find 21².
38. 38.If a − b = 2 and ab = 3, what is a² + b²?
39. 39.Find the value of x² − 2xy + y² when x = 10 and y = 4.
40. 40.Use a² − b² = (a + b)(a − b) to find 35² − 15².

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