Question

Determine the coefficient of the x^{5}y^{7} term in the polynomial expansion of (m + n)^{12}.

- 792
- 439
- 382
- 630

## The correct answer is: 792

STEP BY STEP SOLUTION

Note that the “x” in the binomial has to be chosen 5 times out of 12.

Thus, the coefficient of the term x^{5}y^{7} must be equal to the number of

combinations of 5 objects out of 12: ^{12}C_{5} = 792.

^{5}y

^{7}must be equal to the number of

combinations of 5 objects out of 12:

^{12}C

_{5}= 792.

### Related Questions to study

Find the first four terms of the expansion .

Find the first four terms of the expansion .

If the general term is ^{91}C_{2} x^{89}, what is the expansion?

If the general term is ^{91}C_{2} x^{89}, what is the expansion?

Use polynomial identities to factor each polynomial.

Use polynomial identities to factor each polynomial.

### What is the fourth term of (x – 5y)^{96}?

### What is the fourth term of (x – 5y)^{96}?

Find the coefficient of x^{8} in the expansion of (x + 2)^{11}.

Find the coefficient of x^{8} in the expansion of (x + 2)^{11}.

What do we get after expanding (p + 3q - 2z)^{2}?

What do we get after expanding (p + 3q - 2z)^{2}?

### What do we get after factoring 49x^{2 }- 28xy + .4y^{2}?

### What do we get after factoring 49x^{2 }- 28xy + .4y^{2}?

### _______ is a factor of 4x^{2 }- 9x + 5.

### _______ is a factor of 4x^{2 }- 9x + 5.

### Expand.

### Expand.

### Find the first four terms of the expansion .

### Find the first four terms of the expansion .

### Expand using the binomial theorem.

### Expand using the binomial theorem.

Use polynomial identities to factor each polynomial

Use polynomial identities to factor each polynomial

Determine the independent term of x^{7} in the expansion of (3x^{2} + 4)^{12}.

Determine the independent term of x^{7} in the expansion of (3x^{2} + 4)^{12}.

What do we get after factorizing x^{3}+ 8y^{3}+ z^{3} – 4xyz?

What do we get after factorizing x^{3}+ 8y^{3}+ z^{3} – 4xyz?