# Common Core: High School - Algebra : Using the Binomial Theorem for Expansion: CCSS.Math.Content.HSA-APR.C.5

## Example Questions

### Example Question #1 : Using The Binomial Theorem For Expansion: Ccss.Math.Content.Hsa Apr.C.5

Use Pascal's Triangle to Expand,

Not Possible

Explanation:

In order to do this, we need to recall the formula for Pascal's Triangle.

Since the exponent in the question is 12 we can replace , with 12 .

Now our equation looks like

Now we compute the sum, term by term.

Term 1 :

Term 2 :

Term 3 :

Term 4 :

Term 5 :

Term 6 :

Term 7 :

Term 8 :

Term 9 :

Term 10 :

Term 11 :

Term 12 :

Term 13 :

Now we combine the expressions and we get

### Example Question #2 : Using The Binomial Theorem For Expansion: Ccss.Math.Content.Hsa Apr.C.5

What is the coefficient of  in the expansion of ?

There is no coefficient

Explanation:

In order to do this, we need to recall the formula for Pascal's Triangle.

The part in the expression that we care about is the combination.

We simply do this by looking at the exponent of , and the exponent of the original equation.

In this case  and

Now we compute the following

### Example Question #3 : Using The Binomial Theorem For Expansion: Ccss.Math.Content.Hsa Apr.C.5

Use Pascal's Triangle to Expand

Not Possible

Explanation:

In order to do this, we need to recall the formula for Pascal's Triangle.

Since the exponent in the question is 18 we can replace , with 18 .

Now our equation looks like

Now we compute the sum, term by term.

Term 1 :

Term 2 :

Term 3 :

Term 4 :

Term 5 :

Term 6 :

Term 7 :

Term 8 :

Term 9 :

Term 10 :

Term 11 :

Term 12 :

Term 13 :

Term 14 :

Term 15 :

Term 16 :

Term 17 :

Term 18 :

Term 19 :

Now we combine the expressions and we get

### Example Question #4 : Using The Binomial Theorem For Expansion: Ccss.Math.Content.Hsa Apr.C.5

What is the coefficient of  in the expansion of ?

There is no coefficient

Explanation:

In order to do this, we need to recall the formula for Pascal's Triangle.

The part in the expression that we care about is the combination.

We simply do this by looking at the exponent of , and the exponent of the original equation.

In this case  and

Now we compute the following

### Example Question #5 : Using The Binomial Theorem For Expansion: Ccss.Math.Content.Hsa Apr.C.5

Use Pascal's Triangle to Expand

Not Possible

Explanation:

In order to do this, we need to recall the formula for Pascal's Triangle.

Since the exponent in the question is 8 we can replace , with 8 .

Now our equation looks like

Now we compute the sum, term by term.

Term 1 :

Term 2 :

Term 3 :

Term 4 :

Term 5 :

Term 6 :

Term 7 :

Term 8 :

Term 9 :

Now we combine the expressions and we get

### Example Question #6 : Using The Binomial Theorem For Expansion: Ccss.Math.Content.Hsa Apr.C.5

What is the coefficient of  in the expansion of ?

There is no coefficient

Explanation:

In order to do this, we need to recall the formula for Pascal's Triangle.

The part in the expression that we care about is the combination.

We simply do this by looking at the exponent of , and the exponent of the original equation.

In this case  and

Now we compute the following

### Example Question #7 : Using The Binomial Theorem For Expansion: Ccss.Math.Content.Hsa Apr.C.5

Use Pascal's Triangle to Expand

Not Possible

Explanation:

In order to do this, we need to recall the formula for Pascal's Triangle.

Since the exponent in the question is 7 we can replace , with 7 .

Now our equation looks like

Now we compute the sum, term by term.

Term 1 :

Term 2 :

Term 3 :

Term 4 :

Term 5 :

Term 6 :

Term 7 :

Term 8 :

Now we combine the expressions and we get

### Example Question #8 : Using The Binomial Theorem For Expansion: Ccss.Math.Content.Hsa Apr.C.5

What is the coefficient of  in the expansion of ?

There is no coefficient

Explanation:

In order to do this, we need to recall the formula for Pascal's Triangle.

The part in the expression that we care about is the combination.

We simply do this by looking at the exponent of , and the exponent of the original equation.

In this case  and

Now we compute the following

### Example Question #9 : Using The Binomial Theorem For Expansion: Ccss.Math.Content.Hsa Apr.C.5

Use Pascal's Triangle to Expand

Not Possible

Explanation:

In order to do this, we need to recall the formula for Pascal's Triangle.

Since the exponent in the question is 14 we can replace , with 14 .

Now our equation looks like

Now we compute the sum, term by term.

Term 1 :

Term 2 :

Term 3 :

Term 4 :

Term 5 :

Term 6 :

Term 7 :

Term 8 :

Term 9 :

Term 10 :

Term 11 :

Term 12 :

Term 13 :

Term 14 :

Term 15 :

Now we combine the expressions and we get

### Example Question #10 : Using The Binomial Theorem For Expansion: Ccss.Math.Content.Hsa Apr.C.5

What is the coefficient of  in the expansion of ?

There is no coefficient