Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 133 · 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 26².
2. 2.Use (a − b)² = a² − 2ab + b² to find 47².
3. 3.If a − b = 6 and ab = 16, what is a² + b²?
4. 4.If a + b = 14 and ab = 40, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 93².
6. 6.Use a² − b² = (a + b)(a − b) to find 91² − 65².
7. 7.Use (a + b)² = a² + 2ab + b² to find 39².
8. 8.If a + b = 12 and ab = 32, what is a² + b²?
9. 9.Use (a − b)² = a² − 2ab + b² to find 41².
10. 10.Use (a + b)(a − b) = a² − b² to find 46 × 34.
11. 11.Use (a + b)² = a² + 2ab + b² to find 101².
12. 12.Use (a + b)(a − b) = a² − b² to find 23 × 17.
13. 13.If a + b = 5 and ab = 6, what is a² + b²?
14. 14.If a + b = 4 and ab = 3, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 51².
16. 16.Use a² − b² = (a + b)(a − b) to find 91² − 84².
17. 17.Use (a − b)² = a² − 2ab + b² to find 19².
18. 18.Find the value of x² − y² when x = 15 and y = 10.
19. 19.Use a² − b² = (a + b)(a − b) to find 77² − 41².
20. 20.Use (a + b)² = a² + 2ab + b² to find 61².
21. 21.Use (a + b)(a − b) = a² − b² to find 79 × 61.
22. 22.Use a² − b² = (a + b)(a − b) to find 43² − 1².
23. 23.Use (a + b)² = a² + 2ab + b² to find 54².
24. 24.Use (a + b)(a − b) = a² − b² to find 26 × 14.
25. 25.Find the value of x² − y² when x = 9 and y = 3.
26. 26.Use (a + b)(a − b) = a² − b² to find 88 × 72.
27. 27.Find the value of x² − 2xy + y² when x = 9 and y = 6.
28. 28.Use (a − b)² = a² − 2ab + b² to find 55².
29. 29.Use (a + b)(a − b) = a² − b² to find 107 × 93.
30. 30.Use (a + b)² = a² + 2ab + b² to find 18².
31. 31.If a + b = 21 and ab = 108, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 48 × 32.
33. 33.If a + b = 9 and ab = 20, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 15².
35. 35.If a + b = 18 and ab = 72, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 45².
37. 37.Use a² − b² = (a + b)(a − b) to find 53² − 8².
38. 38.If a − b = 1 and ab = 2, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 36².
40. 40.Use (a + b)² = a² + 2ab + b² to find 73².

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