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

no pictures of the graph

7.25

step-by-step explanation:

we know that 7 equals to 7.0. we also know that 1/4=0.25. so we can add the two together and we get 7.25