Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 143 · 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 = 8 and y = 4.
2. 2.Use (a + b)(a − b) = a² − b² to find 22 × 18.
3. 3.Find the value of x² − 2xy + y² when x = 5 and y = 4.
4. 4.Use (a − b)² = a² − 2ab + b² to find 41².
5. 5.If a + b = 7 and ab = 6, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 18².
7. 7.Use (a + b)² = a² + 2ab + b² to find 104².
8. 8.Use (a + b)² = a² + 2ab + b² to find 96².
9. 9.Find the value of x² − 2xy + y² when x = 10 and y = 3.
10. 10.Use a² − b² = (a + b)(a − b) to find 34² − 24².
11. 11.If a + b = 4 and ab = 3, what is a² + b²?
12. 12.Use (a + b)(a − b) = a² − b² to find 74 × 66.
13. 13.Use a² − b² = (a + b)(a − b) to find 22² − 1².
14. 14.If a + b = 5 and ab = 6, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 91² − 87².
16. 16.Use (a + b)(a − b) = a² − b² to find 101 × 99.
17. 17.Use (a + b)(a − b) = a² − b² to find 108 × 92.
18. 18.Find the value of x² + 2xy + y² when x = 15 and y = 13.
19. 19.Find the value of x² + 2xy + y² when x = 8 and y = 5.
20. 20.Use (a − b)² = a² − 2ab + b² to find 69².
21. 21.If a − b = 3 and ab = 54, what is a² + b²?
22. 22.Find the value of x² + 2xy + y² when x = 11 and y = 7.
23. 23.Use (a + b)(a − b) = a² − b² to find 89 × 71.
24. 24.Use (a + b)² = a² + 2ab + b² to find 38².
25. 25.Use (a + b)(a − b) = a² − b² to find 28 × 12.
26. 26.Use (a + b)² = a² + 2ab + b² to find 41².
27. 27.Use (a + b)² = a² + 2ab + b² to find 93².
28. 28.Use a² − b² = (a + b)(a − b) to find 42² − 38².
29. 29.Use (a + b)² = a² + 2ab + b² to find 44².
30. 30.If a − b = 2 and ab = 120, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 54² − 36².
32. 32.Use (a − b)² = a² − 2ab + b² to find 47².
33. 33.Use (a − b)² = a² − 2ab + b² to find 37².
34. 34.Find the value of x² + 2xy + y² when x = 3 and y = 1.
35. 35.Find the value of x² + 2xy + y² when x = 10 and y = 2.
36. 36.If a + b = 11 and ab = 28, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 31 × 29.
38. 38.Use a² − b² = (a + b)(a − b) to find 71² − 60².
39. 39.If a + b = 17 and ab = 70, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 81².

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