Questions: Simplify: (2 x^3-x+5)-(6 x^3+x^2-x+1) 8 x^3+x^2-2 x+6 -4 x^3-x^2+4 4 x^3-x^2-2 x-4 4 x^3-4

Solution Steps

To simplify the given expression, we need to distribute the negative sign through the second polynomial and then combine like terms.

We start with the expression: \[ (2x^{3} - x + 5) - (6x^{3} + x^{2} - x + 1) \] Distributing the negative sign through the second polynomial gives us: \[ 2x^{3} - x + 5 - 6x^{3} - x^{2} + x - 1 \]

Next, we combine the like terms:

• For \(x^{3}\): \(2x^{3} - 6x^{3} = -4x^{3}\)
• For \(x^{2}\): There is only \(-x^{2}\)
• For \(x\): \(-x + x = 0\)
• For the constant terms: \(5 - 1 = 4\)

Putting it all together, we have: \[ -4x^{3} - x^{2} + 4 \]

Final Answer