Mathematics Worksheet/Algebra/Pascal's Triangle

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 ${\displaystyle \!(\!x+\!y)^{n}}$, exponential results and coefficients.

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

Now do the questions carefully using Pascal's triangle.

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