Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 707 · 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 56 × 44.
2. 2.Use (a + b)(a − b) = a² − b² to find 35 × 25.
3. 3.Use (a + b)(a − b) = a² − b² to find 86 × 74.
4. 4.Use (a + b)(a − b) = a² − b² to find 81 × 79.
5. 5.Find the value of x² − 2xy + y² when x = 11 and y = 2.
6. 6.Find the value of x² − 2xy + y² when x = 10 and y = 6.
7. 7.Use (a + b)(a − b) = a² − b² to find 37 × 23.
8. 8.Use a² − b² = (a + b)(a − b) to find 85² − 40².
9. 9.If a − b = 9 and ab = 10, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 59².
11. 11.Use (a + b)² = a² + 2ab + b² to find 23².
12. 12.Use (a + b)(a − b) = a² − b² to find 23 × 17.
13. 13.Use (a + b)² = a² + 2ab + b² to find 26².
14. 14.Use (a + b)(a − b) = a² − b² to find 33 × 27.
15. 15.Use (a − b)² = a² − 2ab + b² to find 99².
16. 16.Use a² − b² = (a + b)(a − b) to find 27² − 4².
17. 17.Use (a + b)(a − b) = a² − b² to find 31 × 29.
18. 18.If a − b = 3 and ab = 4, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 52².
20. 20.Use (a − b)² = a² − 2ab + b² to find 14².
21. 21.Find the value of x² − y² when x = 3 and y = 1.
22. 22.Use (a − b)² = a² − 2ab + b² to find 98².
23. 23.Use (a − b)² = a² − 2ab + b² to find 18².
24. 24.Find the value of x² − y² when x = 8 and y = 1.
25. 25.Use (a + b)(a − b) = a² − b² to find 71 × 69.
26. 26.Use (a − b)² = a² − 2ab + b² to find 38².
27. 27.If a − b = 2 and ab = 15, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 44².
29. 29.Use (a + b)(a − b) = a² − b² to find 47 × 33.
30. 30.Use (a + b)(a − b) = a² − b² to find 93 × 87.
31. 31.Use a² − b² = (a + b)(a − b) to find 71² − 39².
32. 32.If a + b = 10 and ab = 16, what is a² + b²?
33. 33.If a − b = 5 and ab = 6, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 11².
35. 35.Use (a + b)² = a² + 2ab + b² to find 92².
36. 36.Use a² − b² = (a + b)(a − b) to find 93² − 29².
37. 37.Use a² − b² = (a + b)(a − b) to find 59² − 32².
38. 38.Use (a − b)² = a² − 2ab + b² to find 89².
39. 39.Use (a + b)² = a² + 2ab + b² to find 56².
40. 40.If a − b = 2 and ab = 63, what is a² + b²?

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