Question

Subtract the polynomials. Indicate the degree of the resulting polynomial.
(6x^4y^2-9x^3y-8y) - (12x^4y^2x^3y+3y-12x)

(6x^4y^2-9x^3y-8y) - (12x^4y^2x^3y+3y-12x) = blank

The degree of the resulting polynomial is:

Answer 1

Let's subtract the two polynomials step by step.

We start with the first polynomial:
\[
(6x^4y^2 - 9x^3y - 8y)
\]

Now we need to subtract the second polynomial:
\[
(12x^4y^2 + 3y - 12x)
\]

We can rewrite the subtraction as:
\[
6x^4y^2 - 9x^3y - 8y - (12x^4y^2 + 3y - 12x)
\]

Distributing the negative sign to the second polynomial, we have:
\[
6x^4y^2 - 9x^3y - 8y - 12x^4y^2 - 3y + 12x
\]

Now, we can combine like terms:

1. For \(x^4y^2\):
\[
6x^4y^2 - 12x^4y^2 = -6x^4y^2
\]

2. For \(x^3y\):
\[
-9x^3y \quad (\text{there are no } x^3y \text{ terms to combine})
\]

3. For \(y\):
\[
-8y - 3y = -11y
\]

4. For \(x\):
\[
+12x \quad (\text{there are no other } x \text{ terms to combine})
\]

Putting it all together, we have:
\[
-6x^4y^2 - 9x^3y + 12x - 11y
\]

Now, we can determine the degree of the resulting polynomial. The degree is the highest sum of the exponents of \(x\) and \(y\) in any term.

1. The term \(-6x^4y^2\) has a degree of \(4 + 2 = 6\).
2. The term \(-9x^3y\) has a degree of \(3 + 1 = 4\).
3. The term \(12x\) has a degree of \(1\).
4. The term \(-11y\) has a degree of \(1\).

The highest degree among the terms is \(6\).

Thus, the final result of the subtraction is:
\[
-6x^4y^2 - 9x^3y + 12x - 11y
\]

The degree of the resulting polynomial is:
\[
\text{The degree of the resulting polynomial is: } 6
\]