# 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; Use ^ to write exponentiation.

1

 ${\displaystyle (y+3)^{2}=}$

2

 ${\displaystyle (y-5)^{2}=}$

3

 ${\displaystyle (\Delta +4)^{2}=}$

4

 ${\displaystyle (3x+5)^{3}=}$

5

 ${\displaystyle (4x-2y)^{3}=}$

6

 ${\displaystyle (\alpha +y)^{2}=}$

7

 ${\displaystyle (5x^{2}+3x^{3})^{4}=}$

8

 ${\displaystyle (3x+2y-5z)^{2}=}$

9

 ${\displaystyle (5x^{3}-3y^{5})^{4}=}$

10

 ${\displaystyle (18x+3y^{4})^{6}=}$

11

 ${\displaystyle (a+9)^{3}=}$

12

 ${\displaystyle (b-6)^{5}=}$

13

 ${\displaystyle (6m+3n)^{3}=}$

14

 ${\displaystyle (3x+9y)^{2}=}$

15

 ${\displaystyle (a+b)^{5}=}$

16

 ${\displaystyle (6+y)^{6}=}$

17

 ${\displaystyle (x-8)^{7}=}$

18

 ${\displaystyle (y-6x)^{8}=}$

19

 ${\displaystyle (x+y+z)^{2}=}$

20

 ${\displaystyle (a+b-c+d)^{3}=}$