Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 283 · 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 79².
2. 2.Use a² − b² = (a + b)(a − b) to find 25² − 6².
3. 3.Use (a + b)² = a² + 2ab + b² to find 103².
4. 4.If a + b = 3 and ab = 2, what is a² + b²?
5. 5.Find the value of x² − 2xy + y² when x = 10 and y = 6.
6. 6.Use a² − b² = (a + b)(a − b) to find 71² − 19².
7. 7.Use (a − b)² = a² − 2ab + b² to find 58².
8. 8.Use (a − b)² = a² − 2ab + b² to find 46².
9. 9.If a + b = 19 and ab = 90, what is a² + b²?
10. 10.Use (a + b)(a − b) = a² − b² to find 96 × 84.
11. 11.Use (a − b)² = a² − 2ab + b² to find 77².
12. 12.Use (a + b)(a − b) = a² − b² to find 26 × 14.
13. 13.Use (a − b)² = a² − 2ab + b² to find 28².
14. 14.Find the value of x² + 2xy + y² when x = 12 and y = 1.
15. 15.Use a² − b² = (a + b)(a − b) to find 26² − 7².
16. 16.Use (a + b)(a − b) = a² − b² to find 39 × 21.
17. 17.Use (a − b)² = a² − 2ab + b² to find 29².
18. 18.If a − b = 6 and ab = 16, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 38².
20. 20.Use a² − b² = (a + b)(a − b) to find 68² − 63².
21. 21.Use a² − b² = (a + b)(a − b) to find 91² − 38².
22. 22.Use (a − b)² = a² − 2ab + b² to find 95².
23. 23.Use (a − b)² = a² − 2ab + b² to find 19².
24. 24.Use a² − b² = (a + b)(a − b) to find 85² − 78².
25. 25.Use (a + b)² = a² + 2ab + b² to find 72².
26. 26.Use a² − b² = (a + b)(a − b) to find 64² − 33².
27. 27.Use (a − b)² = a² − 2ab + b² to find 45².
28. 28.Find the value of x² + 2xy + y² when x = 12 and y = 2.
29. 29.Use (a + b)² = a² + 2ab + b² to find 88².
30. 30.Use (a + b)(a − b) = a² − b² to find 36 × 24.
31. 31.If a + b = 5 and ab = 4, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 49².
33. 33.Use (a − b)² = a² − 2ab + b² to find 61².
34. 34.Use a² − b² = (a + b)(a − b) to find 71² − 21².
35. 35.Use (a + b)(a − b) = a² − b² to find 95 × 85.
36. 36.Use (a − b)² = a² − 2ab + b² to find 14².
37. 37.Use a² − b² = (a + b)(a − b) to find 22² − 9².
38. 38.Use (a − b)² = a² − 2ab + b² to find 69².
39. 39.Use (a − b)² = a² − 2ab + b² to find 38².
40. 40.Find the value of x² − 2xy + y² when x = 4 and y = 1.

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