Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 391 · 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 102².
2. 2.Find the value of x² − y² when x = 14 and y = 10.
3. 3.Use (a + b)² = a² + 2ab + b² to find 15².
4. 4.Use (a + b)(a − b) = a² − b² to find 35 × 25.
5. 5.Use (a − b)² = a² − 2ab + b² to find 18².
6. 6.Find the value of x² − 2xy + y² when x = 3 and y = 1.
7. 7.Use (a + b)(a − b) = a² − b² to find 71 × 69.
8. 8.Use a² − b² = (a + b)(a − b) to find 73² − 29².
9. 9.Use (a − b)² = a² − 2ab + b² to find 28².
10. 10.Use (a − b)² = a² − 2ab + b² to find 14².
11. 11.Use (a + b)² = a² + 2ab + b² to find 91².
12. 12.Use a² − b² = (a + b)(a − b) to find 68² − 42².
13. 13.Use a² − b² = (a + b)(a − b) to find 20² − 8².
14. 14.Use (a + b)² = a² + 2ab + b² to find 74².
15. 15.Use (a + b)(a − b) = a² − b² to find 22 × 18.
16. 16.If a + b = 5 and ab = 4, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 52² − 27².
18. 18.Use (a + b)(a − b) = a² − b² to find 33 × 27.
19. 19.Use a² − b² = (a + b)(a − b) to find 51² − 8².
20. 20.Use (a + b)(a − b) = a² − b² to find 41 × 39.
21. 21.Use (a − b)² = a² − 2ab + b² to find 88².
22. 22.Use (a − b)² = a² − 2ab + b² to find 47².
23. 23.Use (a + b)² = a² + 2ab + b² to find 75².
24. 24.If a + b = 12 and ab = 11, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 72 × 68.
26. 26.Use (a + b)(a − b) = a² − b² to find 94 × 86.
27. 27.Use (a + b)² = a² + 2ab + b² to find 32².
28. 28.Use (a + b)² = a² + 2ab + b² to find 57².
29. 29.Use (a + b)(a − b) = a² − b² to find 109 × 91.
30. 30.Use (a − b)² = a² − 2ab + b² to find 49².
31. 31.Use a² − b² = (a + b)(a − b) to find 42² − 4².
32. 32.Use (a + b)² = a² + 2ab + b² to find 43².
33. 33.Find the value of x² + 2xy + y² when x = 5 and y = 1.
34. 34.Use (a + b)(a − b) = a² − b² to find 79 × 61.
35. 35.If a + b = 4 and ab = 3, what is a² + b²?
36. 36.If a + b = 18 and ab = 72, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 67².
38. 38.Use (a + b)(a − b) = a² − b² to find 98 × 82.
39. 39.Use (a − b)² = a² − 2ab + b² to find 63².
40. 40.Use (a + b)(a − b) = a² − b² to find 101 × 99.

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