Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 474 · 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 = 13 and y = 3.
2. 2.Use a² − b² = (a + b)(a − b) to find 29² − 4².
3. 3.Use (a − b)² = a² − 2ab + b² to find 59².
4. 4.Use (a + b)² = a² + 2ab + b² to find 71².
5. 5.Use (a + b)(a − b) = a² − b² to find 54 × 46.
6. 6.Use (a + b)² = a² + 2ab + b² to find 15².
7. 7.If a + b = 20 and ab = 99, what is a² + b²?
8. 8.If a + b = 3 and ab = 2, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 39².
10. 10.Use (a + b)(a − b) = a² − b² to find 34 × 26.
11. 11.Use (a + b)(a − b) = a² − b² to find 61 × 59.
12. 12.Use (a + b)² = a² + 2ab + b² to find 91².
13. 13.Use (a + b)(a − b) = a² − b² to find 35 × 25.
14. 14.Use (a + b)(a − b) = a² − b² to find 92 × 88.
15. 15.Use (a − b)² = a² − 2ab + b² to find 14².
16. 16.Use (a + b)² = a² + 2ab + b² to find 72².
17. 17.Use (a + b)² = a² + 2ab + b² to find 41².
18. 18.If a + b = 8 and ab = 12, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 98².
20. 20.Use (a + b)² = a² + 2ab + b² to find 22².
21. 21.Use (a − b)² = a² − 2ab + b² to find 38².
22. 22.Find the value of x² + 2xy + y² when x = 7 and y = 1.
23. 23.Use (a + b)(a − b) = a² − b² to find 21 × 19.
24. 24.Use (a − b)² = a² − 2ab + b² to find 11².
25. 25.Use (a + b)² = a² + 2ab + b² to find 36².
26. 26.If a − b = 6 and ab = 7, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 57 × 43.
28. 28.Use a² − b² = (a + b)(a − b) to find 21² − 19².
29. 29.Use a² − b² = (a + b)(a − b) to find 79² − 31².
30. 30.If a + b = 6 and ab = 8, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 25².
32. 32.Use (a + b)(a − b) = a² − b² to find 24 × 16.
33. 33.Find the value of x² − y² when x = 12 and y = 2.
34. 34.Use (a + b)(a − b) = a² − b² to find 104 × 96.
35. 35.Use (a + b)² = a² + 2ab + b² to find 38².
36. 36.Find the value of x² + 2xy + y² when x = 7 and y = 2.
37. 37.If a − b = 5 and ab = 6, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 106 × 94.
39. 39.Find the value of x² − 2xy + y² when x = 7 and y = 2.
40. 40.If a + b = 15 and ab = 56, what is a² + b²?

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