Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 116 · 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)(a − b) = a² − b² to find 33 × 27.
2. 2.If a − b = 3 and ab = 18, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 12².
4. 4.Use (a − b)² = a² − 2ab + b² to find 25².
5. 5.Use (a + b)(a − b) = a² − b² to find 36 × 24.
6. 6.If a − b = 3 and ab = 28, what is a² + b²?
7. 7.Find the value of x² + 2xy + y² when x = 15 and y = 6.
8. 8.Use (a + b)(a − b) = a² − b² to find 48 × 32.
9. 9.Use (a − b)² = a² − 2ab + b² to find 35².
10. 10.Use (a + b)(a − b) = a² − b² to find 62 × 58.
11. 11.Use (a + b)(a − b) = a² − b² to find 24 × 16.
12. 12.Use a² − b² = (a + b)(a − b) to find 38² − 34².
13. 13.Use (a + b)² = a² + 2ab + b² to find 41².
14. 14.Use a² − b² = (a + b)(a − b) to find 50² − 12².
15. 15.Use (a + b)² = a² + 2ab + b² to find 83².
16. 16.Use a² − b² = (a + b)(a − b) to find 88² − 50².
17. 17.Find the value of x² + 2xy + y² when x = 12 and y = 4.
18. 18.If a + b = 3 and ab = 2, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 25² − 20².
20. 20.Use (a − b)² = a² − 2ab + b² to find 52².
21. 21.If a − b = 10 and ab = 24, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 86² − 7².
23. 23.Use a² − b² = (a + b)(a − b) to find 50² − 20².
24. 24.Use (a + b)(a − b) = a² − b² to find 99 × 81.
25. 25.Use (a + b)² = a² + 2ab + b² to find 49².
26. 26.Use a² − b² = (a + b)(a − b) to find 85² − 82².
27. 27.Use a² − b² = (a + b)(a − b) to find 73² − 47².
28. 28.Use (a + b)(a − b) = a² − b² to find 102 × 98.
29. 29.Find the value of x² + 2xy + y² when x = 6 and y = 2.
30. 30.Use a² − b² = (a + b)(a − b) to find 72² − 44².
31. 31.Use (a − b)² = a² − 2ab + b² to find 68².
32. 32.Use (a + b)² = a² + 2ab + b² to find 82².
33. 33.Use (a − b)² = a² − 2ab + b² to find 85².
34. 34.Use (a − b)² = a² − 2ab + b² to find 41².
35. 35.Use (a − b)² = a² − 2ab + b² to find 16².
36. 36.Use (a − b)² = a² − 2ab + b² to find 82².
37. 37.Use (a + b)(a − b) = a² − b² to find 76 × 64.
38. 38.Use (a + b)² = a² + 2ab + b² to find 59².
39. 39.Use (a + b)² = a² + 2ab + b² to find 64².
40. 40.Use (a − b)² = a² − 2ab + b² to find 99².

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