Question

# Dakota said the third term of the expansions of .Explain Dakota’s error and then correct the answer.

Hint:

### The binomial expansion is , here n ≥ 0 . We are asked to describe and correct the mistake Dakota made in the expansion of the expression .

## The correct answer is: 4C2

Step 1 of 2:

The given expression is , here x = 2g & y = 3h.

Thus, the expansion would be:

Step 2 of 2:

Analyzing the expansion, find the coefficient of g^{2}h^{2}. The value is: 216 Dakota got the wrong answer because she did not count the value 4C_{2} .

Step 2 of 2:

Analyzing the expansion, find the coefficient of g

^{2}h

^{2}. The value is: 216 Dakota got the wrong answer because she did not count the value 4C

_{2}.

You can use Both the Pascal’s triangle and binomial expansion to find the value of (x + y)n .

### Related Questions to study

### What number does C3 represent in the expansion ? Explain.

The value is called the combination permutation.

### What number does C3 represent in the expansion ? Explain.

The value is called the combination permutation.

### Explain how to use a polynomial identity to factor .

### Explain how to use a polynomial identity to factor .

### Use polynomial identities to factor the polynomials or simplify the expressions :

### Use polynomial identities to factor the polynomials or simplify the expressions :

### How are Pascal’s triangle and binomial expansion such as related?

### How are Pascal’s triangle and binomial expansion such as related?

### Explain how to use a polynomial identity to factor .

We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.

### Explain how to use a polynomial identity to factor .

We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.

### Use polynomial identities to factor the polynomials or simplify the expressions :

### Use polynomial identities to factor the polynomials or simplify the expressions :

### Explain why the middle term is 10x.

### Explain why the middle term is 10x.

### Use polynomial identities to factor the polynomials or simplify the expressions :

### Use polynomial identities to factor the polynomials or simplify the expressions :

### How can you use polynomial identities to rewrite expressions efficiently ?

### How can you use polynomial identities to rewrite expressions efficiently ?

### Use binomial theorem to expand

### Use binomial theorem to expand

### Use polynomial identities to factor the polynomials or simplify the expressions :

### Use polynomial identities to factor the polynomials or simplify the expressions :

### Use binomial theorem to expand .

### Use binomial theorem to expand .

### Use polynomial identities to factor the polynomials or simplify the expressions :

### Use polynomial identities to factor the polynomials or simplify the expressions :

### How are Pascal’s triangle and binomial expansion such as (a + b)^{5} related?

You can find the expansion of (x + y)n using both Pascal’s triangle and binomial expansion.

### How are Pascal’s triangle and binomial expansion such as (a + b)^{5} related?

You can find the expansion of (x + y)n using both Pascal’s triangle and binomial expansion.