Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 383 · 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 67².
2. 2.Find the value of x² + 2xy + y² when x = 3 and y = 2.
3. 3.Use a² − b² = (a + b)(a − b) to find 79² − 66².
4. 4.Use (a − b)² = a² − 2ab + b² to find 48².
5. 5.Use a² − b² = (a + b)(a − b) to find 62² − 38².
6. 6.If a − b = 7 and ab = 8, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 61².
8. 8.Use (a − b)² = a² − 2ab + b² to find 46².
9. 9.Use (a − b)² = a² − 2ab + b² to find 51².
10. 10.Use (a − b)² = a² − 2ab + b² to find 91².
11. 11.If a + b = 10 and ab = 16, what is a² + b²?
12. 12.Use (a + b)(a − b) = a² − b² to find 37 × 23.
13. 13.Find the value of x² + 2xy + y² when x = 4 and y = 3.
14. 14.Use (a + b)(a − b) = a² − b² to find 94 × 86.
15. 15.If a + b = 20 and ab = 99, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 105 × 95.
17. 17.If a − b = 7 and ab = 30, what is a² + b²?
18. 18.Find the value of x² − 2xy + y² when x = 15 and y = 10.
19. 19.Use (a + b)² = a² + 2ab + b² to find 66².
20. 20.Use (a + b)² = a² + 2ab + b² to find 82².
21. 21.Use (a − b)² = a² − 2ab + b² to find 98².
22. 22.Use (a + b)² = a² + 2ab + b² to find 51².
23. 23.Use a² − b² = (a + b)(a − b) to find 44² − 2².
24. 24.Use (a − b)² = a² − 2ab + b² to find 72².
25. 25.Use (a + b)(a − b) = a² − b² to find 75 × 65.
26. 26.Use (a + b)² = a² + 2ab + b² to find 37².
27. 27.Use (a + b)(a − b) = a² − b² to find 49 × 31.
28. 28.Use (a + b)² = a² + 2ab + b² to find 108².
29. 29.Use (a + b)(a − b) = a² − b² to find 104 × 96.
30. 30.Use (a − b)² = a² − 2ab + b² to find 63².
31. 31.Use a² − b² = (a + b)(a − b) to find 52² − 40².
32. 32.Use (a + b)(a − b) = a² − b² to find 33 × 27.
33. 33.Use (a + b)(a − b) = a² − b² to find 96 × 84.
34. 34.Use (a + b)(a − b) = a² − b² to find 46 × 34.
35. 35.Use (a + b)² = a² + 2ab + b² to find 32².
36. 36.Use (a + b)(a − b) = a² − b² to find 107 × 93.
37. 37.Use (a − b)² = a² − 2ab + b² to find 34².
38. 38.Use (a + b)² = a² + 2ab + b² to find 52².
39. 39.Use a² − b² = (a + b)(a − b) to find 30² − 20².
40. 40.Use (a + b)(a − b) = a² − b² to find 31 × 29.

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