Mathematics Worksheet/Algebra/Pascal's Triangle

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Study the Pascal's Triangle below.

                                         1
                                       1   1
                                     1   2   1
                                   1   3   3   1
                                 1   4   6   4   1
                               1   5  10  10   5   1


This table showing the \!(\!x+\!y)^n, exponential results and coefficients.

\!(\!x+\!y)^n Exponential results Coefficients
\!(\!x+\!y) \!x+\!y 1 1
\!(\!x+\!y)^2 \!x^2+\!2xy+\!y^2 1 2 1
\!(\!x+\!y)^3 \!x^3+\!3x^2y+\!3xy^2+\!y^3 1 3 3 1
\!(\!x+\!y)^4 \!x^4+\!4x^3y+\!6x^2y^2+\!4xy^3+\!y^4 1 4 6 4 1
\!(\!x+\!y)^5 \!x^5+\!5x^4y+\!10x^3y^2+\!10x^2y^3+\!5xy^4+\!y^5 1 5 10 10 5 1

Now do the questions carefully using Pascal's triangle.

  1. \!(\!y+\!3)^2=\cdots
  2. \!(\!y-\!5)^2=\cdots
  3. \!(\Delta+\!4)^2=\cdots
  4. \!(\!3x+\!5)^3=\cdots
  5. \!(\!4x-\!2y)^3=\cdots
  6. \!(\alpha+\!y)^2=\cdots
  7. \!(\!5x^2+3x^3)^4=\cdots
  8. \!(\!3x+\!2y-\!5z)^2=\cdots
  9. \!(\!5x^3-\!3y^5)^4=\cdots
  10. \!(\!18x+\!3y^4)^6=\cdots
  11. \!(\!a+\!9)^3=\cdots
  12. \!(\!b-\!6)^5=\cdots
  13. \!(\!6m+\!3n)^3=\cdots
  14. \!(\!3x+\!9y)^2=\cdots
  15. \!(\!a+\!b)^5=\cdots
  16. \!(\!6+\!y)^6=\cdots
  17. \!(\!x-\!8)^7=\cdots
  18. \!(\!y-\!6x)^8=\cdots
  19. \!(\!x+\!y+\!z)^2=\cdots
  20. \!(\!a+\!b-\!c+\!d)^3=\cdots