Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 746 · 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 27 × 13.
2. 2.Use (a − b)² = a² − 2ab + b² to find 69².
3. 3.Find the value of x² − y² when x = 7 and y = 5.
4. 4.Use (a + b)² = a² + 2ab + b² to find 69².
5. 5.Use (a + b)(a − b) = a² − b² to find 24 × 16.
6. 6.Find the value of x² + 2xy + y² when x = 15 and y = 10.
7. 7.Use (a + b)² = a² + 2ab + b² to find 79².
8. 8.If a − b = 2 and ab = 3, what is a² + b²?
9. 9.If a + b = 17 and ab = 72, what is a² + b²?
10. 10.Find the value of x² + 2xy + y² when x = 5 and y = 1.
11. 11.Use (a − b)² = a² − 2ab + b² to find 99².
12. 12.Use a² − b² = (a + b)(a − b) to find 55² − 33².
13. 13.Use (a − b)² = a² − 2ab + b² to find 16².
14. 14.Use a² − b² = (a + b)(a − b) to find 89² − 70².
15. 15.Use (a + b)(a − b) = a² − b² to find 96 × 84.
16. 16.Find the value of x² − y² when x = 5 and y = 3.
17. 17.If a − b = 7 and ab = 8, what is a² + b²?
18. 18.Use a² − b² = (a + b)(a − b) to find 76² − 26².
19. 19.Use (a + b)² = a² + 2ab + b² to find 21².
20. 20.Use (a + b)(a − b) = a² − b² to find 33 × 27.
21. 21.Use (a + b)² = a² + 2ab + b² to find 23².
22. 22.Use a² − b² = (a + b)(a − b) to find 26² − 15².
23. 23.Use (a + b)² = a² + 2ab + b² to find 39².
24. 24.Use (a + b)(a − b) = a² − b² to find 87 × 73.
25. 25.Use (a + b)² = a² + 2ab + b² to find 44².
26. 26.Use (a + b)² = a² + 2ab + b² to find 32².
27. 27.Use a² − b² = (a + b)(a − b) to find 36² − 25².
28. 28.Use a² − b² = (a + b)(a − b) to find 46² − 33².
29. 29.Find the value of x² − y² when x = 10 and y = 4.
30. 30.Use (a + b)(a − b) = a² − b² to find 22 × 18.
31. 31.Find the value of x² + 2xy + y² when x = 6 and y = 1.
32. 32.Use (a + b)² = a² + 2ab + b² to find 18².
33. 33.Use (a + b)² = a² + 2ab + b² to find 37².
34. 34.If a + b = 3 and ab = 2, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 75 × 65.
36. 36.If a + b = 8 and ab = 12, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 65 × 55.
38. 38.Use (a + b)² = a² + 2ab + b² to find 28².
39. 39.If a − b = 1 and ab = 110, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 43 × 37.

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