Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 630 · 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 = 5 and ab = 36, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 27².
3. 3.Use (a − b)² = a² − 2ab + b² to find 39².
4. 4.Find the value of x² + 2xy + y² when x = 14 and y = 10.
5. 5.Use a² − b² = (a + b)(a − b) to find 76² − 61².
6. 6.Use (a + b)(a − b) = a² − b² to find 62 × 58.
7. 7.Use (a + b)(a − b) = a² − b² to find 37 × 23.
8. 8.Use a² − b² = (a + b)(a − b) to find 25² − 1².
9. 9.Use a² − b² = (a + b)(a − b) to find 84² − 46².
10. 10.Use (a + b)(a − b) = a² − b² to find 85 × 75.
11. 11.If a + b = 7 and ab = 10, what is a² + b²?
12. 12.Use (a − b)² = a² − 2ab + b² to find 68².
13. 13.Use (a − b)² = a² − 2ab + b² to find 52².
14. 14.Use (a − b)² = a² − 2ab + b² to find 31².
15. 15.Use (a + b)(a − b) = a² − b² to find 61 × 59.
16. 16.If a − b = 2 and ab = 3, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 42².
18. 18.Use (a + b)² = a² + 2ab + b² to find 85².
19. 19.Use (a − b)² = a² − 2ab + b² to find 86².
20. 20.Use (a + b)² = a² + 2ab + b² to find 75².
21. 21.Use (a − b)² = a² − 2ab + b² to find 19².
22. 22.Find the value of x² + 2xy + y² when x = 5 and y = 1.
23. 23.Use (a + b)² = a² + 2ab + b² to find 24².
24. 24.Use (a − b)² = a² − 2ab + b² to find 74².
25. 25.If a + b = 3 and ab = 2, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 107 × 93.
27. 27.Use (a + b)(a − b) = a² − b² to find 47 × 33.
28. 28.Find the value of x² + 2xy + y² when x = 14 and y = 1.
29. 29.Use (a − b)² = a² − 2ab + b² to find 15².
30. 30.Use (a − b)² = a² − 2ab + b² to find 17².
31. 31.If a + b = 11 and ab = 10, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 79².
33. 33.Use a² − b² = (a + b)(a − b) to find 48² − 4².
34. 34.Use (a + b)(a − b) = a² − b² to find 38 × 22.
35. 35.Use (a + b)(a − b) = a² − b² to find 26 × 14.
36. 36.Find the value of x² − y² when x = 8 and y = 2.
37. 37.Use (a + b)(a − b) = a² − b² to find 79 × 61.
38. 38.Use (a + b)² = a² + 2ab + b² to find 31².
39. 39.Use (a + b)(a − b) = a² − b² to find 65 × 55.
40. 40.Use (a + b)² = a² + 2ab + b² to find 82².

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