Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 364 · 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 = 8 and y = 5.
2. 2.Use (a − b)² = a² − 2ab + b² to find 98².
3. 3.Use a² − b² = (a + b)(a − b) to find 78² − 71².
4. 4.Find the value of x² − y² when x = 6 and y = 3.
5. 5.Find the value of x² − 2xy + y² when x = 3 and y = 2.
6. 6.If a − b = 1 and ab = 2, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 49².
8. 8.Use (a + b)(a − b) = a² − b² to find 25 × 15.
9. 9.Find the value of x² − y² when x = 11 and y = 9.
10. 10.Use (a − b)² = a² − 2ab + b² to find 31².
11. 11.Use (a + b)(a − b) = a² − b² to find 31 × 29.
12. 12.Use (a + b)² = a² + 2ab + b² to find 19².
13. 13.Use (a + b)(a − b) = a² − b² to find 99 × 81.
14. 14.Use (a + b)(a − b) = a² − b² to find 51 × 49.
15. 15.Use (a + b)(a − b) = a² − b² to find 94 × 86.
16. 16.Find the value of x² − y² when x = 9 and y = 7.
17. 17.Use (a − b)² = a² − 2ab + b² to find 36².
18. 18.Find the value of x² + 2xy + y² when x = 7 and y = 4.
19. 19.Use (a + b)(a − b) = a² − b² to find 75 × 65.
20. 20.Use (a − b)² = a² − 2ab + b² to find 48².
21. 21.Find the value of x² + 2xy + y² when x = 10 and y = 9.
22. 22.Find the value of x² − 2xy + y² when x = 9 and y = 6.
23. 23.Find the value of x² + 2xy + y² when x = 12 and y = 4.
24. 24.Use (a + b)² = a² + 2ab + b² to find 71².
25. 25.Find the value of x² − 2xy + y² when x = 7 and y = 6.
26. 26.Use (a + b)² = a² + 2ab + b² to find 99².
27. 27.Use (a − b)² = a² − 2ab + b² to find 74².
28. 28.Use a² − b² = (a + b)(a − b) to find 35² − 20².
29. 29.Use (a + b)² = a² + 2ab + b² to find 65².
30. 30.Use a² − b² = (a + b)(a − b) to find 47² − 42².
31. 31.If a − b = 3 and ab = 28, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 71².
33. 33.If a + b = 6 and ab = 8, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 101 × 99.
35. 35.Use (a − b)² = a² − 2ab + b² to find 66².
36. 36.Use (a + b)(a − b) = a² − b² to find 45 × 35.
37. 37.Use (a − b)² = a² − 2ab + b² to find 92².
38. 38.Use (a + b)² = a² + 2ab + b² to find 11².
39. 39.Use (a + b)(a − b) = a² − b² to find 104 × 96.
40. 40.Use a² − b² = (a + b)(a − b) to find 85² − 21².

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