Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 893 · 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 − 88².
2. 2.Use (a − b)² = a² − 2ab + b² to find 59².
3. 3.Use a² − b² = (a + b)(a − b) to find 78² − 23².
4. 4.Use (a + b)² = a² + 2ab + b² to find 58².
5. 5.Use (a + b)(a − b) = a² − b² to find 33 × 27.
6. 6.Use a² − b² = (a + b)(a − b) to find 26² − 5².
7. 7.Use (a + b)(a − b) = a² − b² to find 45 × 35.
8. 8.Use (a + b)² = a² + 2ab + b² to find 87².
9. 9.Find the value of x² − y² when x = 12 and y = 4.
10. 10.Use a² − b² = (a + b)(a − b) to find 51² − 40².
11. 11.Use (a + b)² = a² + 2ab + b² to find 19².
12. 12.Use (a + b)(a − b) = a² − b² to find 52 × 48.
13. 13.Use (a + b)² = a² + 2ab + b² to find 94².
14. 14.Use a² − b² = (a + b)(a − b) to find 64² − 39².
15. 15.Use (a + b)² = a² + 2ab + b² to find 25².
16. 16.Use (a + b)(a − b) = a² − b² to find 21 × 19.
17. 17.Use (a + b)² = a² + 2ab + b² to find 32².
18. 18.Use (a − b)² = a² − 2ab + b² to find 88².
19. 19.If a + b = 15 and ab = 50, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 79².
21. 21.Use (a + b)² = a² + 2ab + b² to find 103².
22. 22.If a + b = 15 and ab = 44, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 21².
24. 24.Use (a + b)² = a² + 2ab + b² to find 62².
25. 25.Find the value of x² + 2xy + y² when x = 4 and y = 1.
26. 26.Use a² − b² = (a + b)(a − b) to find 96² − 1².
27. 27.Find the value of x² + 2xy + y² when x = 6 and y = 4.
28. 28.Use (a − b)² = a² − 2ab + b² to find 22².
29. 29.Use (a + b)² = a² + 2ab + b² to find 72².
30. 30.If a − b = 1 and ab = 12, what is a² + b²?
31. 31.If a − b = 7 and ab = 30, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 15².
33. 33.If a + b = 15 and ab = 36, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 48 × 32.
35. 35.Use (a + b)(a − b) = a² − b² to find 41 × 39.
36. 36.If a − b = 7 and ab = 8, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 92².
38. 38.Use (a + b)² = a² + 2ab + b² to find 49².
39. 39.Use (a − b)² = a² − 2ab + b² to find 56².
40. 40.Use a² − b² = (a + b)(a − b) to find 32² − 4².

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