Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 315 · 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 21 × 19.
2. 2.Find the value of x² + 2xy + y² when x = 10 and y = 5.
3. 3.Use (a − b)² = a² − 2ab + b² to find 12².
4. 4.Use a² − b² = (a + b)(a − b) to find 47² − 37².
5. 5.Find the value of x² − 2xy + y² when x = 13 and y = 8.
6. 6.Use (a + b)² = a² + 2ab + b² to find 21².
7. 7.If a + b = 13 and ab = 42, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 93² − 28².
9. 9.Find the value of x² + 2xy + y² when x = 3 and y = 2.
10. 10.If a + b = 6 and ab = 5, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 54².
12. 12.Use (a + b)² = a² + 2ab + b² to find 18².
13. 13.Use (a + b)² = a² + 2ab + b² to find 91².
14. 14.Use (a + b)(a − b) = a² − b² to find 34 × 26.
15. 15.Use (a − b)² = a² − 2ab + b² to find 84².
16. 16.If a − b = 1 and ab = 2, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 88² − 6².
18. 18.Use a² − b² = (a + b)(a − b) to find 97² − 14².
19. 19.If a − b = 11 and ab = 12, what is a² + b²?
20. 20.If a − b = 4 and ab = 12, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 63² − 31².
22. 22.Find the value of x² + 2xy + y² when x = 13 and y = 4.
23. 23.If a + b = 4 and ab = 3, what is a² + b²?
24. 24.Use a² − b² = (a + b)(a − b) to find 71² − 6².
25. 25.Use (a + b)² = a² + 2ab + b² to find 14².
26. 26.Use (a + b)² = a² + 2ab + b² to find 65².
27. 27.Use (a + b)² = a² + 2ab + b² to find 59².
28. 28.Find the value of x² + 2xy + y² when x = 9 and y = 2.
29. 29.Use (a + b)² = a² + 2ab + b² to find 104².
30. 30.Use a² − b² = (a + b)(a − b) to find 64² − 19².
31. 31.Use (a + b)(a − b) = a² − b² to find 26 × 14.
32. 32.Use (a + b)(a − b) = a² − b² to find 106 × 94.
33. 33.Use (a − b)² = a² − 2ab + b² to find 17².
34. 34.If a + b = 3 and ab = 2, what is a² + b²?
35. 35.Find the value of x² − 2xy + y² when x = 9 and y = 1.
36. 36.Find the value of x² + 2xy + y² when x = 13 and y = 11.
37. 37.Use (a − b)² = a² − 2ab + b² to find 55².
38. 38.Use a² − b² = (a + b)(a − b) to find 59² − 14².
39. 39.Use (a + b)(a − b) = a² − b² to find 82 × 78.
40. 40.Use (a + b)² = a² + 2ab + b² to find 38².

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