Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 620 · 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 52².
2. 2.Find the value of x² + 2xy + y² when x = 4 and y = 2.
3. 3.Find the value of x² − y² when x = 7 and y = 4.
4. 4.Find the value of x² − 2xy + y² when x = 12 and y = 4.
5. 5.If a − b = 5 and ab = 14, what is a² + b²?
6. 6.If a + b = 12 and ab = 27, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 12².
8. 8.Use a² − b² = (a + b)(a − b) to find 72² − 29².
9. 9.Use (a + b)² = a² + 2ab + b² to find 103².
10. 10.Use (a + b)² = a² + 2ab + b² to find 69².
11. 11.Use (a + b)(a − b) = a² − b² to find 99 × 81.
12. 12.Find the value of x² + 2xy + y² when x = 4 and y = 3.
13. 13.Find the value of x² − y² when x = 11 and y = 2.
14. 14.Use a² − b² = (a + b)(a − b) to find 84² − 24².
15. 15.Use a² − b² = (a + b)(a − b) to find 24² − 5².
16. 16.Use (a − b)² = a² − 2ab + b² to find 22².
17. 17.Use (a − b)² = a² − 2ab + b² to find 98².
18. 18.Use (a + b)(a − b) = a² − b² to find 37 × 23.
19. 19.Use a² − b² = (a + b)(a − b) to find 29² − 26².
20. 20.Use (a − b)² = a² − 2ab + b² to find 38².
21. 21.Use (a − b)² = a² − 2ab + b² to find 63².
22. 22.Use (a − b)² = a² − 2ab + b² to find 13².
23. 23.Use (a + b)(a − b) = a² − b² to find 92 × 88.
24. 24.Use (a + b)² = a² + 2ab + b² to find 101².
25. 25.Use (a + b)² = a² + 2ab + b² to find 16².
26. 26.Find the value of x² − y² when x = 3 and y = 2.
27. 27.Use (a + b)² = a² + 2ab + b² to find 55².
28. 28.Use (a + b)(a − b) = a² − b² to find 85 × 75.
29. 29.Use (a + b)² = a² + 2ab + b² to find 82².
30. 30.Use (a + b)(a − b) = a² − b² to find 67 × 53.
31. 31.Use (a + b)² = a² + 2ab + b² to find 109².
32. 32.Use (a + b)(a − b) = a² − b² to find 35 × 25.
33. 33.Use a² − b² = (a + b)(a − b) to find 63² − 1².
34. 34.Find the value of x² − 2xy + y² when x = 3 and y = 2.
35. 35.Use (a − b)² = a² − 2ab + b² to find 75².
36. 36.Use (a − b)² = a² − 2ab + b² to find 49².
37. 37.Find the value of x² + 2xy + y² when x = 12 and y = 3.
38. 38.Use (a + b)² = a² + 2ab + b² to find 38².
39. 39.Find the value of x² − 2xy + y² when x = 6 and y = 5.
40. 40.Use a² − b² = (a + b)(a − b) to find 30² − 4².

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