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
$(x+y)^{3}$	$x^{3}+3x^{2}y+3xy^{2}+y^{3}$	1 3 3 1
$(x+y)^{4}$	$x^{4}+4x^{3}y+6x^{2}y^{2}+4xy^{3}+y^{4}$	1 4 6 4 1
$(x+y)^{5}$	$x^{5}+5x^{4}y+10x^{3}y^{2}+10x^{2}y^{3}+5xy^{4}+y^{5}$	1 5 10 10 5 1

Now do the questions carefully using Pascal's triangle; Use ^ to write exponentiation.

α Δ

1

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

2

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

3

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

4

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

5

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

6

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

7

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

8

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

9

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

10

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

11

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

12

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

13

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

14

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

15

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

16

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

17

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

18

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

19

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

20

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