Questions: Simplify: (7 x^3 + x^2 + 2 x - 8) - (-8 x^3 - 6 x^2 + 2)

Solution Steps

To simplify the given expression, we need to distribute the negative sign across the terms in 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: \[ (7x^{3} + x^{2} + 2x - 8) - (-8x^{3} - 6x^{2} + 2) \] Distributing the negative sign gives us: \[ 7x^{3} + x^{2} + 2x - 8 + 8x^{3} + 6x^{2} - 2 \]

Next, we combine the like terms:

• For \(x^{3}\): \(7x^{3} + 8x^{3} = 15x^{3}\)
• For \(x^{2}\): \(x^{2} + 6x^{2} = 7x^{2}\)
• For \(x\): \(2x\) remains as is.
• For the constant terms: \(-8 - 2 = -10\)

Thus, the simplified expression is: \[ 15x^{3} + 7x^{2} + 2x - 10 \]

Final Answer