Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 250 · 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 89².
2. 2.If a − b = 3 and ab = 10, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 41².
4. 4.Use (a + b)(a − b) = a² − b² to find 33 × 27.
5. 5.Use a² − b² = (a + b)(a − b) to find 62² − 60².
6. 6.Use (a − b)² = a² − 2ab + b² to find 24².
7. 7.If a + b = 8 and ab = 12, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 68 × 52.
9. 9.Use (a + b)(a − b) = a² − b² to find 43 × 37.
10. 10.Use (a + b)² = a² + 2ab + b² to find 56².
11. 11.Use (a + b)(a − b) = a² − b² to find 24 × 16.
12. 12.If a + b = 8 and ab = 15, what is a² + b²?
13. 13.Find the value of x² + 2xy + y² when x = 15 and y = 6.
14. 14.Use (a + b)(a − b) = a² − b² to find 88 × 72.
15. 15.Use (a + b)(a − b) = a² − b² to find 44 × 36.
16. 16.Use (a + b)(a − b) = a² − b² to find 106 × 94.
17. 17.Use a² − b² = (a + b)(a − b) to find 47² − 9².
18. 18.Use (a + b)² = a² + 2ab + b² to find 87².
19. 19.Use (a + b)(a − b) = a² − b² to find 25 × 15.
20. 20.Use a² − b² = (a + b)(a − b) to find 46² − 13².
21. 21.Use a² − b² = (a + b)(a − b) to find 77² − 58².
22. 22.If a + b = 12 and ab = 11, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 97 × 83.
24. 24.Find the value of x² + 2xy + y² when x = 3 and y = 2.
25. 25.Find the value of x² − y² when x = 4 and y = 1.
26. 26.If a − b = 3 and ab = 108, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 75 × 65.
28. 28.Use (a − b)² = a² − 2ab + b² to find 82².
29. 29.If a − b = 3 and ab = 54, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 58² − 10².
31. 31.Find the value of x² + 2xy + y² when x = 7 and y = 2.
32. 32.If a + b = 3 and ab = 2, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 97².
34. 34.If a − b = 4 and ab = 5, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 93² − 56².
36. 36.Use a² − b² = (a + b)(a − b) to find 24² − 16².
37. 37.If a + b = 13 and ab = 22, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 48².
39. 39.If a − b = 3 and ab = 88, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 25² − 6².

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