# 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 $\!(\!x+\!y)^n$, 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. $\!(\!a+\!b-\!c+\!d)^3=\cdots$