Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 433 · 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 93² − 20².
2. 2.Use (a + b)² = a² + 2ab + b² to find 63².
3. 3.If a − b = 5 and ab = 24, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 61².
5. 5.Use a² − b² = (a + b)(a − b) to find 58² − 13².
6. 6.Use (a + b)(a − b) = a² − b² to find 39 × 21.
7. 7.Find the value of x² − y² when x = 3 and y = 2.
8. 8.Use (a − b)² = a² − 2ab + b² to find 18².
9. 9.Use a² − b² = (a + b)(a − b) to find 61² − 6².
10. 10.If a − b = 6 and ab = 16, what is a² + b²?
11. 11.If a − b = 2 and ab = 99, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 55² − 6².
13. 13.Use (a − b)² = a² − 2ab + b² to find 27².
14. 14.Use (a − b)² = a² − 2ab + b² to find 92².
15. 15.Use (a − b)² = a² − 2ab + b² to find 42².
16. 16.Use a² − b² = (a + b)(a − b) to find 28² − 18².
17. 17.Use (a − b)² = a² − 2ab + b² to find 65².
18. 18.Use (a − b)² = a² − 2ab + b² to find 59².
19. 19.Use (a + b)(a − b) = a² − b² to find 74 × 66.
20. 20.Find the value of x² − 2xy + y² when x = 9 and y = 6.
21. 21.Use (a + b)² = a² + 2ab + b² to find 39².
22. 22.If a + b = 7 and ab = 12, what is a² + b²?
23. 23.Use (a + b)² = a² + 2ab + b² to find 59².
24. 24.If a + b = 3 and ab = 2, what is a² + b²?
25. 25.Find the value of x² + 2xy + y² when x = 12 and y = 7.
26. 26.If a + b = 14 and ab = 45, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 42².
28. 28.Use (a + b)(a − b) = a² − b² to find 73 × 67.
29. 29.Find the value of x² − 2xy + y² when x = 15 and y = 5.
30. 30.Use (a + b)(a − b) = a² − b² to find 38 × 22.
31. 31.Find the value of x² − y² when x = 15 and y = 10.
32. 32.If a + b = 5 and ab = 4, what is a² + b²?
33. 33.If a − b = 1 and ab = 132, what is a² + b²?
34. 34.If a − b = 1 and ab = 2, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 56 × 44.
36. 36.Use (a + b)(a − b) = a² − b² to find 96 × 84.
37. 37.Use (a + b)² = a² + 2ab + b² to find 52².
38. 38.Use (a + b)² = a² + 2ab + b² to find 96².
39. 39.Use (a − b)² = a² − 2ab + b² to find 94².
40. 40.Use (a − b)² = a² − 2ab + b² to find 84².

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