Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 982 · 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)(a − b) = a² − b² to find 25 × 15.
2. 2.Use a² − b² = (a + b)(a − b) to find 99² − 7².
3. 3.Use (a + b)(a − b) = a² − b² to find 43 × 37.
4. 4.If a − b = 4 and ab = 77, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 91².
6. 6.Find the value of x² + 2xy + y² when x = 6 and y = 1.
7. 7.Use (a + b)(a − b) = a² − b² to find 64 × 56.
8. 8.Use (a + b)(a − b) = a² − b² to find 67 × 53.
9. 9.Use (a + b)² = a² + 2ab + b² to find 57².
10. 10.Use (a + b)² = a² + 2ab + b² to find 41².
11. 11.Use (a + b)² = a² + 2ab + b² to find 78².
12. 12.Find the value of x² − y² when x = 14 and y = 6.
13. 13.Use (a + b)² = a² + 2ab + b² to find 79².
14. 14.Use (a + b)² = a² + 2ab + b² to find 47².
15. 15.Use (a − b)² = a² − 2ab + b² to find 28².
16. 16.Use (a + b)(a − b) = a² − b² to find 65 × 55.
17. 17.Use (a + b)(a − b) = a² − b² to find 57 × 43.
18. 18.Use (a + b)(a − b) = a² − b² to find 107 × 93.
19. 19.Use (a − b)² = a² − 2ab + b² to find 34².
20. 20.If a − b = 2 and ab = 3, what is a² + b²?
21. 21.If a + b = 13 and ab = 36, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 93².
23. 23.Use (a + b)(a − b) = a² − b² to find 74 × 66.
24. 24.Use (a + b)² = a² + 2ab + b² to find 103².
25. 25.Use (a + b)(a − b) = a² − b² to find 31 × 29.
26. 26.Use (a − b)² = a² − 2ab + b² to find 13².
27. 27.Use (a − b)² = a² − 2ab + b² to find 69².
28. 28.Use (a + b)² = a² + 2ab + b² to find 38².
29. 29.Use (a − b)² = a² − 2ab + b² to find 21².
30. 30.Use a² − b² = (a + b)(a − b) to find 87² − 63².
31. 31.Use (a − b)² = a² − 2ab + b² to find 36².
32. 32.Use (a + b)² = a² + 2ab + b² to find 27².
33. 33.Use a² − b² = (a + b)(a − b) to find 51² − 9².
34. 34.Use (a − b)² = a² − 2ab + b² to find 44².
35. 35.Use (a + b)² = a² + 2ab + b² to find 37².
36. 36.Use (a + b)² = a² + 2ab + b² to find 69².
37. 37.If a + b = 5 and ab = 6, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 25².
39. 39.Use a² − b² = (a + b)(a − b) to find 55² − 45².
40. 40.Use (a − b)² = a² − 2ab + b² to find 29².

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