Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 624 · 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.Find the value of x² + 2xy + y² when x = 11 and y = 9.
2. 2.Use (a − b)² = a² − 2ab + b² to find 39².
3. 3.Use (a − b)² = a² − 2ab + b² to find 67².
4. 4.Use (a + b)² = a² + 2ab + b² to find 106².
5. 5.Find the value of x² + 2xy + y² when x = 6 and y = 1.
6. 6.Use (a − b)² = a² − 2ab + b² to find 72².
7. 7.Use (a + b)² = a² + 2ab + b² to find 59².
8. 8.Use (a − b)² = a² − 2ab + b² to find 93².
9. 9.Find the value of x² − 2xy + y² when x = 12 and y = 2.
10. 10.Use (a + b)(a − b) = a² − b² to find 32 × 28.
11. 11.Use (a + b)² = a² + 2ab + b² to find 87².
12. 12.Use a² − b² = (a + b)(a − b) to find 43² − 41².
13. 13.Use (a + b)(a − b) = a² − b² to find 62 × 58.
14. 14.Use (a + b)² = a² + 2ab + b² to find 42².
15. 15.Use a² − b² = (a + b)(a − b) to find 82² − 59².
16. 16.Use (a + b)² = a² + 2ab + b² to find 82².
17. 17.Find the value of x² − 2xy + y² when x = 12 and y = 7.
18. 18.If a − b = 1 and ab = 110, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 24².
20. 20.If a − b = 3 and ab = 18, what is a² + b²?
21. 21.Use (a + b)² = a² + 2ab + b² to find 21².
22. 22.Use (a + b)(a − b) = a² − b² to find 65 × 55.
23. 23.Use (a + b)(a − b) = a² − b² to find 21 × 19.
24. 24.If a − b = 4 and ab = 60, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 85².
26. 26.Use (a − b)² = a² − 2ab + b² to find 29².
27. 27.If a + b = 5 and ab = 6, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 52² − 2².
29. 29.Use a² − b² = (a + b)(a − b) to find 88² − 40².
30. 30.Use (a − b)² = a² − 2ab + b² to find 86².
31. 31.Use a² − b² = (a + b)(a − b) to find 63² − 40².
32. 32.If a + b = 3 and ab = 2, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 19².
34. 34.Use (a + b)(a − b) = a² − b² to find 89 × 71.
35. 35.Use (a + b)(a − b) = a² − b² to find 47 × 33.
36. 36.If a + b = 10 and ab = 21, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 81².
38. 38.Use (a + b)(a − b) = a² − b² to find 88 × 72.
39. 39.Use (a + b)(a − b) = a² − b² to find 54 × 46.
40. 40.Use (a − b)² = a² − 2ab + b² to find 23².

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