Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 402 · 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 18².
2. 2.Use (a + b)(a − b) = a² − b² to find 61 × 59.
3. 3.If a − b = 5 and ab = 14, what is a² + b²?
4. 4.Find the value of x² − 2xy + y² when x = 15 and y = 12.
5. 5.Use (a + b)(a − b) = a² − b² to find 99 × 81.
6. 6.If a − b = 1 and ab = 2, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 34².
8. 8.Use (a + b)² = a² + 2ab + b² to find 78².
9. 9.Find the value of x² + 2xy + y² when x = 15 and y = 2.
10. 10.Use (a + b)(a − b) = a² − b² to find 25 × 15.
11. 11.Find the value of x² − y² when x = 4 and y = 1.
12. 12.Use a² − b² = (a + b)(a − b) to find 21² − 19².
13. 13.Use (a + b)² = a² + 2ab + b² to find 98².
14. 14.Use (a + b)² = a² + 2ab + b² to find 105².
15. 15.Use (a + b)(a − b) = a² − b² to find 65 × 55.
16. 16.Use (a + b)(a − b) = a² − b² to find 33 × 27.
17. 17.Use a² − b² = (a + b)(a − b) to find 76² − 42².
18. 18.If a − b = 4 and ab = 96, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 21².
20. 20.Use (a − b)² = a² − 2ab + b² to find 84².
21. 21.Use (a − b)² = a² − 2ab + b² to find 41².
22. 22.If a − b = 3 and ab = 108, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 98 × 82.
24. 24.If a − b = 6 and ab = 72, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 43² − 6².
26. 26.Use (a + b)² = a² + 2ab + b² to find 54².
27. 27.Use (a + b)² = a² + 2ab + b² to find 21².
28. 28.Use (a − b)² = a² − 2ab + b² to find 63².
29. 29.Use (a − b)² = a² − 2ab + b² to find 29².
30. 30.If a + b = 11 and ab = 24, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 53 × 47.
32. 32.Use (a + b)² = a² + 2ab + b² to find 55².
33. 33.Use (a − b)² = a² − 2ab + b² to find 23².
34. 34.Use (a + b)(a − b) = a² − b² to find 36 × 24.
35. 35.Find the value of x² + 2xy + y² when x = 9 and y = 6.
36. 36.Use (a − b)² = a² − 2ab + b² to find 68².
37. 37.Use (a + b)(a − b) = a² − b² to find 42 × 38.
38. 38.Use (a − b)² = a² − 2ab + b² to find 45².
39. 39.Use (a − b)² = a² − 2ab + b² to find 59².
40. 40.Find the value of x² − 2xy + y² when x = 10 and y = 3.

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