Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 712 · 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 54².
2. 2.Use (a + b)² = a² + 2ab + b² to find 99².
3. 3.Use (a − b)² = a² − 2ab + b² to find 48².
4. 4.Use a² − b² = (a + b)(a − b) to find 81² − 37².
5. 5.Find the value of x² − 2xy + y² when x = 3 and y = 2.
6. 6.Use (a − b)² = a² − 2ab + b² to find 51².
7. 7.If a + b = 4 and ab = 3, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 89².
9. 9.Use a² − b² = (a + b)(a − b) to find 57² − 19².
10. 10.Use (a − b)² = a² − 2ab + b² to find 12².
11. 11.Use (a + b)(a − b) = a² − b² to find 42 × 38.
12. 12.Use (a + b)(a − b) = a² − b² to find 98 × 82.
13. 13.Find the value of x² + 2xy + y² when x = 9 and y = 2.
14. 14.Use (a + b)² = a² + 2ab + b² to find 32².
15. 15.Find the value of x² + 2xy + y² when x = 6 and y = 4.
16. 16.If a − b = 3 and ab = 4, what is a² + b²?
17. 17.Use (a + b)(a − b) = a² − b² to find 109 × 91.
18. 18.Use a² − b² = (a + b)(a − b) to find 58² − 45².
19. 19.Find the value of x² − y² when x = 7 and y = 4.
20. 20.Use (a + b)(a − b) = a² − b² to find 84 × 76.
21. 21.Use (a − b)² = a² − 2ab + b² to find 64².
22. 22.Use (a + b)(a − b) = a² − b² to find 35 × 25.
23. 23.Use a² − b² = (a + b)(a − b) to find 62² − 26².
24. 24.Use (a + b)(a − b) = a² − b² to find 92 × 88.
25. 25.Use (a + b)² = a² + 2ab + b² to find 15².
26. 26.Find the value of x² + 2xy + y² when x = 8 and y = 2.
27. 27.Find the value of x² − y² when x = 5 and y = 4.
28. 28.Use (a + b)(a − b) = a² − b² to find 93 × 87.
29. 29.Find the value of x² − y² when x = 4 and y = 3.
30. 30.Find the value of x² + 2xy + y² when x = 13 and y = 3.
31. 31.If a − b = 2 and ab = 3, what is a² + b²?
32. 32.Find the value of x² − 2xy + y² when x = 10 and y = 9.
33. 33.Use (a + b)² = a² + 2ab + b² to find 63².
34. 34.Use (a + b)(a − b) = a² − b² to find 31 × 29.
35. 35.Find the value of x² − 2xy + y² when x = 14 and y = 3.
36. 36.Use (a + b)² = a² + 2ab + b² to find 41².
37. 37.Use a² − b² = (a + b)(a − b) to find 46² − 8².
38. 38.Use (a + b)² = a² + 2ab + b² to find 21².
39. 39.Find the value of x² − y² when x = 5 and y = 1.
40. 40.Use (a + b)² = a² + 2ab + b² to find 71².

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