Questions: Subtract. Your answer should be a polynomial in standard form. [ (-5 m^2-8)-(-3 m^2+m+2)= ]

Solution Steps

To subtract the given polynomials, distribute the negative sign across the second polynomial and then combine like terms. This involves adding or subtracting the coefficients of terms with the same degree.

We start with the expression: \[ \left(-5 m^{2}-8\right)-\left(-3 m^{2}+m+2\right) \] Distributing the negative sign across the second polynomial gives: \[ -5 m^{2} - 8 + 3 m^{2} - m - 2 \]

Next, we combine the like terms:

• For \(m^{2}\) terms: \(-5 m^{2} + 3 m^{2} = -2 m^{2}\)
• For \(m\) terms: There is only \(-m\)
• For constant terms: \(-8 - 2 = -10\)

Thus, the expression simplifies to: \[ -2 m^{2} - m - 10 \]

Final Answer