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

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