Question

which statement is true about the polynomial -10m⁴n³ + 8m²n⁶ + 3m⁴n³ - 2m²n⁶ - 6m²n⁶ after it has been fully simplified?
○ it is a monomial with a degree of 4.
○ it is a monomial with a degree of 7.
○ it is a binomial with a degree of 6.
○ it is a binomial with a degree of 8.

Explanation:

Step1: Combine like terms for \(m^4n^3\) terms

The terms with \(m^4n^3\) are \(-10m^4n^3\) and \(3m^4n^3\). Combining them: \(-10m^4n^3 + 3m^4n^3 = (-10 + 3)m^4n^3 = -7m^4n^3\).

Step2: Combine like terms for \(m^2n^6\) terms

The terms with \(m^2n^6\) are \(8m^2n^6\), \(-2m^2n^6\), and \(-6m^2n^6\). Combining them: \(8m^2n^6 - 2m^2n^6 - 6m^2n^6=(8 - 2 - 6)m^2n^6 = 0m^2n^6\) (which cancels out).

Step3: Simplify the polynomial

After combining like terms, the polynomial simplifies to \(-7m^4n^3\), which is a monomial.

Step4: Find the degree of the monomial

The degree of a monomial \(a x^p y^q\) is \(p + q\). For \(-7m^4n^3\), the degree is \(4 + 3 = 7\).

Answer:

It is a monomial with a degree of 7.