Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 216 · 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 a² − b² = (a + b)(a − b) to find 29² − 5².
2. 2.Use (a + b)(a − b) = a² − b² to find 22 × 18.
3. 3.Find the value of x² + 2xy + y² when x = 14 and y = 6.
4. 4.Find the value of x² + 2xy + y² when x = 9 and y = 6.
5. 5.Use a² − b² = (a + b)(a − b) to find 79² − 9².
6. 6.Use a² − b² = (a + b)(a − b) to find 20² − 15².
7. 7.Use a² − b² = (a + b)(a − b) to find 92² − 20².
8. 8.Find the value of x² − 2xy + y² when x = 11 and y = 3.
9. 9.Use (a + b)² = a² + 2ab + b² to find 93².
10. 10.Use (a − b)² = a² − 2ab + b² to find 44².
11. 11.Find the value of x² − 2xy + y² when x = 4 and y = 1.
12. 12.Find the value of x² + 2xy + y² when x = 10 and y = 4.
13. 13.Find the value of x² − y² when x = 3 and y = 2.
14. 14.If a − b = 1 and ab = 2, what is a² + b²?
15. 15.Find the value of x² + 2xy + y² when x = 5 and y = 4.
16. 16.Find the value of x² + 2xy + y² when x = 6 and y = 1.
17. 17.Use (a − b)² = a² − 2ab + b² to find 45².
18. 18.Use (a − b)² = a² − 2ab + b² to find 62².
19. 19.Use (a − b)² = a² − 2ab + b² to find 88².
20. 20.Find the value of x² − y² when x = 8 and y = 3.
21. 21.Use (a + b)(a − b) = a² − b² to find 84 × 76.
22. 22.If a + b = 7 and ab = 10, what is a² + b²?
23. 23.If a − b = 3 and ab = 4, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 62 × 58.
25. 25.Use (a + b)(a − b) = a² − b² to find 102 × 98.
26. 26.Use (a − b)² = a² − 2ab + b² to find 49².
27. 27.Use (a + b)² = a² + 2ab + b² to find 99².
28. 28.Use (a + b)(a − b) = a² − b² to find 73 × 67.
29. 29.Find the value of x² + 2xy + y² when x = 3 and y = 2.
30. 30.Use (a + b)(a − b) = a² − b² to find 36 × 24.
31. 31.Use (a + b)(a − b) = a² − b² to find 49 × 31.
32. 32.Find the value of x² + 2xy + y² when x = 3 and y = 1.
33. 33.If a − b = 7 and ab = 44, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 24².
35. 35.If a + b = 4 and ab = 3, what is a² + b²?
36. 36.Use a² − b² = (a + b)(a − b) to find 84² − 74².
37. 37.Find the value of x² + 2xy + y² when x = 4 and y = 1.
38. 38.Use (a + b)² = a² + 2ab + b² to find 49².
39. 39.Use a² − b² = (a + b)(a − b) to find 85² − 19².
40. 40.Use (a + b)(a − b) = a² − b² to find 35 × 25.

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