Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 663 · 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 = 4 and y = 2.
2. 2.Use (a − b)² = a² − 2ab + b² to find 35².
3. 3.Use (a + b)² = a² + 2ab + b² to find 54².
4. 4.Use (a + b)² = a² + 2ab + b² to find 36².
5. 5.Use (a + b)² = a² + 2ab + b² to find 34².
6. 6.If a + b = 10 and ab = 9, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 27².
8. 8.Use (a + b)² = a² + 2ab + b² to find 33².
9. 9.Use (a + b)(a − b) = a² − b² to find 53 × 47.
10. 10.Find the value of x² − 2xy + y² when x = 13 and y = 4.
11. 11.If a − b = 4 and ab = 32, what is a² + b²?
12. 12.Use (a − b)² = a² − 2ab + b² to find 24².
13. 13.If a − b = 5 and ab = 36, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 37² − 35².
15. 15.Use (a − b)² = a² − 2ab + b² to find 33².
16. 16.Find the value of x² − 2xy + y² when x = 5 and y = 2.
17. 17.Use (a + b)² = a² + 2ab + b² to find 94².
18. 18.Use a² − b² = (a + b)(a − b) to find 84² − 27².
19. 19.Use (a + b)² = a² + 2ab + b² to find 18².
20. 20.Use a² − b² = (a + b)(a − b) to find 72² − 1².
21. 21.Use (a + b)(a − b) = a² − b² to find 93 × 87.
22. 22.Find the value of x² − 2xy + y² when x = 3 and y = 1.
23. 23.Use a² − b² = (a + b)(a − b) to find 99² − 4².
24. 24.Use (a + b)² = a² + 2ab + b² to find 65².
25. 25.Use (a + b)(a − b) = a² − b² to find 76 × 64.
26. 26.Use a² − b² = (a + b)(a − b) to find 73² − 3².
27. 27.Find the value of x² − y² when x = 9 and y = 2.
28. 28.Use (a + b)² = a² + 2ab + b² to find 17².
29. 29.Use (a + b)(a − b) = a² − b² to find 52 × 48.
30. 30.Use (a + b)(a − b) = a² − b² to find 62 × 58.
31. 31.If a − b = 2 and ab = 3, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 15².
33. 33.If a − b = 5 and ab = 24, what is a² + b²?
34. 34.If a + b = 16 and ab = 55, what is a² + b²?
35. 35.Find the value of x² + 2xy + y² when x = 10 and y = 5.
36. 36.Use a² − b² = (a + b)(a − b) to find 90² − 72².
37. 37.Use (a − b)² = a² − 2ab + b² to find 74².
38. 38.Use (a + b)(a − b) = a² − b² to find 42 × 38.
39. 39.Use (a + b)² = a² + 2ab + b² to find 63².
40. 40.Use (a − b)² = a² − 2ab + b² to find 34².

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