Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 205 · 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 55² − 34².
2. 2.Use (a + b)² = a² + 2ab + b² to find 46².
3. 3.If a − b = 3 and ab = 88, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 33².
5. 5.Use a² − b² = (a + b)(a − b) to find 31² − 9².
6. 6.Use (a + b)² = a² + 2ab + b² to find 43².
7. 7.Use (a + b)² = a² + 2ab + b² to find 74².
8. 8.Use (a + b)² = a² + 2ab + b² to find 37².
9. 9.Find the value of x² + 2xy + y² when x = 7 and y = 4.
10. 10.Find the value of x² − y² when x = 3 and y = 1.
11. 11.If a + b = 14 and ab = 24, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 36² − 10².
13. 13.Use (a + b)(a − b) = a² − b² to find 24 × 16.
14. 14.Use a² − b² = (a + b)(a − b) to find 25² − 9².
15. 15.If a + b = 13 and ab = 30, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 40² − 26².
17. 17.Use (a + b)² = a² + 2ab + b² to find 103².
18. 18.Use (a + b)(a − b) = a² − b² to find 86 × 74.
19. 19.If a − b = 2 and ab = 3, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 62².
21. 21.Use (a − b)² = a² − 2ab + b² to find 24².
22. 22.Use (a + b)(a − b) = a² − b² to find 62 × 58.
23. 23.Use (a + b)² = a² + 2ab + b² to find 92².
24. 24.Use a² − b² = (a + b)(a − b) to find 59² − 23².
25. 25.Use a² − b² = (a + b)(a − b) to find 40² − 21².
26. 26.Find the value of x² − 2xy + y² when x = 3 and y = 1.
27. 27.Find the value of x² − 2xy + y² when x = 15 and y = 10.
28. 28.Use (a + b)(a − b) = a² − b² to find 87 × 73.
29. 29.Use (a − b)² = a² − 2ab + b² to find 48².
30. 30.Use (a − b)² = a² − 2ab + b² to find 89².
31. 31.Use (a − b)² = a² − 2ab + b² to find 77².
32. 32.Use (a + b)(a − b) = a² − b² to find 35 × 25.
33. 33.If a + b = 11 and ab = 24, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 101 × 99.
35. 35.Use a² − b² = (a + b)(a − b) to find 47² − 2².
36. 36.If a − b = 1 and ab = 12, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 107 × 93.
38. 38.Use (a − b)² = a² − 2ab + b² to find 22².
39. 39.Use (a + b)² = a² + 2ab + b² to find 22².
40. 40.Use (a + b)(a − b) = a² − b² to find 98 × 82.

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