Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 843 · 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.If a − b = 1 and ab = 42, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 73².
3. 3.Use a² − b² = (a + b)(a − b) to find 67² − 30².
4. 4.Find the value of x² + 2xy + y² when x = 15 and y = 2.
5. 5.Use (a + b)(a − b) = a² − b² to find 58 × 42.
6. 6.Use a² − b² = (a + b)(a − b) to find 34² − 5².
7. 7.Find the value of x² + 2xy + y² when x = 5 and y = 4.
8. 8.Use a² − b² = (a + b)(a − b) to find 69² − 8².
9. 9.Use a² − b² = (a + b)(a − b) to find 55² − 32².
10. 10.Use (a + b)² = a² + 2ab + b² to find 101².
11. 11.Use a² − b² = (a + b)(a − b) to find 38² − 16².
12. 12.Use (a − b)² = a² − 2ab + b² to find 35².
13. 13.If a + b = 17 and ab = 72, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 31².
15. 15.Use (a + b)(a − b) = a² − b² to find 95 × 85.
16. 16.If a − b = 2 and ab = 15, what is a² + b²?
17. 17.Find the value of x² + 2xy + y² when x = 8 and y = 2.
18. 18.Use a² − b² = (a + b)(a − b) to find 20² − 5².
19. 19.Use (a + b)(a − b) = a² − b² to find 35 × 25.
20. 20.Find the value of x² + 2xy + y² when x = 5 and y = 1.
21. 21.Find the value of x² + 2xy + y² when x = 3 and y = 2.
22. 22.Use (a + b)² = a² + 2ab + b² to find 26².
23. 23.Use (a + b)² = a² + 2ab + b² to find 108².
24. 24.Use (a + b)² = a² + 2ab + b² to find 27².
25. 25.Use (a + b)² = a² + 2ab + b² to find 79².
26. 26.Use a² − b² = (a + b)(a − b) to find 98² − 58².
27. 27.Use (a + b)² = a² + 2ab + b² to find 68².
28. 28.Use (a + b)(a − b) = a² − b² to find 49 × 31.
29. 29.Use a² − b² = (a + b)(a − b) to find 33² − 10².
30. 30.Find the value of x² − y² when x = 13 and y = 2.
31. 31.Use a² − b² = (a + b)(a − b) to find 94² − 3².
32. 32.Use (a + b)² = a² + 2ab + b² to find 33².
33. 33.Use (a + b)(a − b) = a² − b² to find 65 × 55.
34. 34.Use (a − b)² = a² − 2ab + b² to find 34².
35. 35.Find the value of x² − 2xy + y² when x = 6 and y = 1.
36. 36.Use (a + b)² = a² + 2ab + b² to find 16².
37. 37.Use (a + b)(a − b) = a² − b² to find 88 × 72.
38. 38.Use a² − b² = (a + b)(a − b) to find 41² − 14².
39. 39.Use (a + b)² = a² + 2ab + b² to find 84².
40. 40.Use (a + b)(a − b) = a² − b² to find 109 × 91.

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