When using the binomial formula, which of the following is a correct step in the expansion of (x+y)^4

Step-by-step explanation:

Use the binomial expansion theorem to find each term. The binomial theorem states  

(

a

+

b

)

n

=

n

∑

k

=

0

n

C

k

⋅

(

a

n

−

k

b

k

)

.

4

∑

k

=

0

4

!

(

4

−

k

)

!

k

!

⋅

(

x

)

4

−

k

⋅

(

y

)

k

Expand the summation.

4

!

(

4

−

0

)

!

0

!

(

x

)

4

−

0

⋅

(

y

)

0

+

4

!

(

4

−

1

)

!

1

!

(

x

)

4

−

1

⋅

(

y

)

+

4

!

(

4

−

2

)

!

2

!

(

x

)

4

−

2

⋅

(

y

)

2

+

4

!

(

4

−

3

)

!

3

!

(

x

)

4

−

3

⋅

(

y

)

3

+

4

!

(

4

−

4

)

!

4

!

(

x

)

4

−

4

⋅

(

y

)

4

Simplify the exponents for each term of the expansion.

1

⋅

(

x

)

4

⋅

(

y

)

0

+

4

⋅

(

x

)

3

⋅

(

y

)

+

6

⋅

(

x

)

2

⋅

(

y

)

2

+

4

⋅

(

x

)

⋅

(

y

)

3

+

1

⋅

(

x

)

0

⋅

(

y

)

4

Simplify each term.

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x

4

+

4

x

3

y

+

6

x

2

y

2

+

4

x

y

3

+

y

4

s

step-by-step explanation: