Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 342 · 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 93 × 87.
2. 2.Use a² − b² = (a + b)(a − b) to find 25² − 24².
3. 3.Find the value of x² + 2xy + y² when x = 9 and y = 4.
4. 4.Use (a + b)(a − b) = a² − b² to find 89 × 71.
5. 5.Find the value of x² + 2xy + y² when x = 15 and y = 2.
6. 6.Use (a + b)(a − b) = a² − b² to find 73 × 67.
7. 7.Use a² − b² = (a + b)(a − b) to find 61² − 31².
8. 8.Use (a + b)² = a² + 2ab + b² to find 71².
9. 9.Use a² − b² = (a + b)(a − b) to find 66² − 50².
10. 10.Use a² − b² = (a + b)(a − b) to find 69² − 20².
11. 11.Use (a + b)² = a² + 2ab + b² to find 87².
12. 12.Use (a + b)² = a² + 2ab + b² to find 104².
13. 13.Use (a − b)² = a² − 2ab + b² to find 87².
14. 14.Use (a − b)² = a² − 2ab + b² to find 18².
15. 15.Find the value of x² + 2xy + y² when x = 15 and y = 8.
16. 16.If a − b = 1 and ab = 2, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 98².
18. 18.Use (a − b)² = a² − 2ab + b² to find 77².
19. 19.Use (a + b)² = a² + 2ab + b² to find 25².
20. 20.Use (a + b)² = a² + 2ab + b² to find 99².
21. 21.Use (a + b)(a − b) = a² − b² to find 27 × 13.
22. 22.Find the value of x² − y² when x = 11 and y = 1.
23. 23.Find the value of x² − y² when x = 12 and y = 3.
24. 24.If a − b = 4 and ab = 45, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 29².
26. 26.If a + b = 4 and ab = 3, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 57² − 23².
28. 28.Use (a + b)(a − b) = a² − b² to find 95 × 85.
29. 29.Use a² − b² = (a + b)(a − b) to find 77² − 8².
30. 30.If a + b = 22 and ab = 120, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 33².
32. 32.Use a² − b² = (a + b)(a − b) to find 40² − 36².
33. 33.Use a² − b² = (a + b)(a − b) to find 32² − 5².
34. 34.Find the value of x² − 2xy + y² when x = 4 and y = 3.
35. 35.Use (a + b)² = a² + 2ab + b² to find 98².
36. 36.Use (a + b)(a − b) = a² − b² to find 47 × 33.
37. 37.Use (a + b)² = a² + 2ab + b² to find 85².
38. 38.Use a² − b² = (a + b)(a − b) to find 66² − 61².
39. 39.Use (a − b)² = a² − 2ab + b² to find 42².
40. 40.Use a² − b² = (a + b)(a − b) to find 78² − 68².

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