Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 886 · 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 33².
2. 2.Find the value of x² + 2xy + y² when x = 3 and y = 1.
3. 3.If a + b = 8 and ab = 7, what is a² + b²?
4. 4.Find the value of x² − 2xy + y² when x = 3 and y = 2.
5. 5.Use a² − b² = (a + b)(a − b) to find 66² − 48².
6. 6.Use (a + b)(a − b) = a² − b² to find 33 × 27.
7. 7.Use (a − b)² = a² − 2ab + b² to find 51².
8. 8.Use (a + b)² = a² + 2ab + b² to find 41².
9. 9.Use (a + b)(a − b) = a² − b² to find 101 × 99.
10. 10.If a + b = 17 and ab = 66, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 88² − 22².
12. 12.Use (a + b)(a − b) = a² − b² to find 39 × 21.
13. 13.Use (a + b)(a − b) = a² − b² to find 83 × 77.
14. 14.Use a² − b² = (a + b)(a − b) to find 45² − 42².
15. 15.Use a² − b² = (a + b)(a − b) to find 52² − 24².
16. 16.If a + b = 21 and ab = 110, what is a² + b²?
17. 17.If a − b = 5 and ab = 66, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 65².
19. 19.Use (a + b)² = a² + 2ab + b² to find 19².
20. 20.If a − b = 2 and ab = 8, what is a² + b²?
21. 21.Use (a + b)² = a² + 2ab + b² to find 29².
22. 22.If a − b = 2 and ab = 24, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 24² − 1².
24. 24.Use (a + b)(a − b) = a² − b² to find 78 × 62.
25. 25.Use (a + b)(a − b) = a² − b² to find 44 × 36.
26. 26.Use (a + b)(a − b) = a² − b² to find 25 × 15.
27. 27.Use (a + b)(a − b) = a² − b² to find 87 × 73.
28. 28.If a + b = 9 and ab = 14, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 59² − 38².
30. 30.Find the value of x² + 2xy + y² when x = 7 and y = 2.
31. 31.Use (a − b)² = a² − 2ab + b² to find 98².
32. 32.Use (a − b)² = a² − 2ab + b² to find 52².
33. 33.Use a² − b² = (a + b)(a − b) to find 63² − 54².
34. 34.Use a² − b² = (a + b)(a − b) to find 63² − 19².
35. 35.Use a² − b² = (a + b)(a − b) to find 92² − 26².
36. 36.Use (a + b)² = a² + 2ab + b² to find 69².
37. 37.Use a² − b² = (a + b)(a − b) to find 34² − 26².
38. 38.Use (a − b)² = a² − 2ab + b² to find 25².
39. 39.If a − b = 1 and ab = 12, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 18².

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