Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 752 · 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 88².
2. 2.Use (a − b)² = a² − 2ab + b² to find 75².
3. 3.Use (a − b)² = a² − 2ab + b² to find 22².
4. 4.Use (a + b)² = a² + 2ab + b² to find 45².
5. 5.Use (a + b)(a − b) = a² − b² to find 61 × 59.
6. 6.If a + b = 5 and ab = 6, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 91² − 51².
8. 8.Use (a + b)(a − b) = a² − b² to find 25 × 15.
9. 9.Use a² − b² = (a + b)(a − b) to find 55² − 26².
10. 10.Use (a − b)² = a² − 2ab + b² to find 12².
11. 11.Use (a + b)² = a² + 2ab + b² to find 17².
12. 12.Find the value of x² + 2xy + y² when x = 14 and y = 12.
13. 13.Find the value of x² + 2xy + y² when x = 8 and y = 6.
14. 14.If a + b = 10 and ab = 21, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 101².
16. 16.If a − b = 8 and ab = 33, what is a² + b²?
17. 17.If a − b = 3 and ab = 54, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 18².
19. 19.Use (a + b)² = a² + 2ab + b² to find 104².
20. 20.If a + b = 6 and ab = 8, what is a² + b²?
21. 21.If a + b = 5 and ab = 4, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 87² − 4².
23. 23.If a + b = 8 and ab = 12, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 85².
25. 25.Use (a + b)² = a² + 2ab + b² to find 46².
26. 26.Find the value of x² + 2xy + y² when x = 13 and y = 8.
27. 27.Find the value of x² + 2xy + y² when x = 12 and y = 3.
28. 28.Use (a − b)² = a² − 2ab + b² to find 74².
29. 29.Use (a + b)(a − b) = a² − b² to find 79 × 61.
30. 30.Use (a + b)(a − b) = a² − b² to find 105 × 95.
31. 31.Use (a − b)² = a² − 2ab + b² to find 38².
32. 32.Use (a + b)(a − b) = a² − b² to find 101 × 99.
33. 33.Find the value of x² + 2xy + y² when x = 9 and y = 7.
34. 34.If a + b = 10 and ab = 24, what is a² + b²?
35. 35.Find the value of x² − 2xy + y² when x = 13 and y = 10.
36. 36.Find the value of x² − y² when x = 9 and y = 5.
37. 37.If a + b = 17 and ab = 70, what is a² + b²?
38. 38.If a − b = 9 and ab = 36, what is a² + b²?
39. 39.Find the value of x² − y² when x = 10 and y = 5.
40. 40.Use (a + b)² = a² + 2ab + b² to find 68².

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