Expand the following using the Binomial Theorem and Pascal’s triangle (2x − 3y)^4

Step-by-step explanation:

Pascal's Triangle can be displayed as such:

1

1

−

1

1

−

2

−

1

1

−

3

−

3

−

1

1

−

4

−

6

−

4

−

1

The triangle can be used to calculate the coefficients of the expansion of  

(

a

+

b

)

n

by taking the exponent  

n

and adding  

1

. The coefficients will correspond with line  

n

+

1

of the triangle. For  

(

2

x

−

3

y

)

4

,  

n

=

4

so the coefficients of the expansion will correspond with line  

5

.

The expansion follows the rule  

(

a

+

b

)

n

=

c

0

a

n

b

0

+

c

1

a

n

−

1

b

1

+

c

n

−

1

a

1

b

n

−

1

+

c

n

a

0

b

n

. The values of the coefficients, from the triangle, are  

1

−

4

−

6

−

4

−

1

.

1

a

4

b

0

+

4

a

3

b

+

6

a

2

b

2

+

4

a

b

3

+

1

a

0

b

4

Substitute the actual values of  

a

2

x

and  

b

−

3

y

into the expression.

1

(

2

x

)

4

(

−

3

y

)

0

+

4

(

2

x

)

3

(

−

3

y

)

1

+

6

(

2

x

)

2

(

−

3

y

)

2

+

4

(

2

x

)

1

(

−

3

y

)

3

+

1

(

2

x

)

0

(

−

3

y

)

4

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.

c

step-by-step explanation: