Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 810 · 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.If a + b = 6 and ab = 5, what is a² + b²?
2. 2.Use (a + b)(a − b) = a² − b² to find 92 × 88.
3. 3.Use (a − b)² = a² − 2ab + b² to find 77².
4. 4.If a + b = 13 and ab = 22, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 79².
6. 6.Find the value of x² + 2xy + y² when x = 7 and y = 3.
7. 7.If a + b = 3 and ab = 2, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 34².
9. 9.Find the value of x² − y² when x = 10 and y = 2.
10. 10.Use (a + b)(a − b) = a² − b² to find 35 × 25.
11. 11.Use (a − b)² = a² − 2ab + b² to find 14².
12. 12.Use (a + b)² = a² + 2ab + b² to find 75².
13. 13.Use a² − b² = (a + b)(a − b) to find 71² − 63².
14. 14.Use (a + b)² = a² + 2ab + b² to find 109².
15. 15.Use a² − b² = (a + b)(a − b) to find 46² − 34².
16. 16.Use (a + b)(a − b) = a² − b² to find 44 × 36.
17. 17.Use (a − b)² = a² − 2ab + b² to find 79².
18. 18.If a − b = 3 and ab = 10, what is a² + b²?
19. 19.Use (a + b)(a − b) = a² − b² to find 91 × 89.
20. 20.Use (a + b)(a − b) = a² − b² to find 36 × 24.
21. 21.Use (a + b)(a − b) = a² − b² to find 28 × 12.
22. 22.If a − b = 6 and ab = 7, what is a² + b²?
23. 23.Find the value of x² + 2xy + y² when x = 14 and y = 4.
24. 24.Find the value of x² − y² when x = 5 and y = 4.
25. 25.Use (a − b)² = a² − 2ab + b² to find 88².
26. 26.Use a² − b² = (a + b)(a − b) to find 20² − 19².
27. 27.Use a² − b² = (a + b)(a − b) to find 32² − 19².
28. 28.Find the value of x² − y² when x = 3 and y = 2.
29. 29.Use (a − b)² = a² − 2ab + b² to find 75².
30. 30.Use a² − b² = (a + b)(a − b) to find 75² − 41².
31. 31.If a + b = 4 and ab = 3, what is a² + b²?
32. 32.If a − b = 2 and ab = 63, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 74 × 66.
34. 34.Use (a − b)² = a² − 2ab + b² to find 63².
35. 35.Use (a + b)² = a² + 2ab + b² to find 82².
36. 36.Use (a − b)² = a² − 2ab + b² to find 35².
37. 37.If a − b = 11 and ab = 12, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 56 × 44.
39. 39.Use (a − b)² = a² − 2ab + b² to find 19².
40. 40.Use (a − b)² = a² − 2ab + b² to find 37².

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