# 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.

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

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