Find the difference: (3x^3-2x^2+4x-8)-(5x^3+12x^2-3x-4) 3x^3-2x^2+4x-8+square Combine like terms square -5x^3-12x^2+3x+4 -5x^3-12x^2-3x-4 5x^3+12x^2+3x+4 5x^3+12x^2-3x-4 : 8x^3-10x^2+7x+4 -8x^3-10x^2+x-12 -2x^3-14x^2+7x-4 : -2x^6-14x^4+x^2-12

To solve the problem, we need to find the difference between the two polynomials:<br /><br />\[<br />(3x^3 - 2x^2 + 4x - 8) - (5x^3 + 12x^2 - 3x - 4).<br />\]<br /><br />### Step 1: Distribute the negative sign<br />When subtracting a polynomial, distribute the negative sign across all terms in the second polynomial:<br /><br />\[<br />3x^3 - 2x^2 + 4x - 8 - (5x^3 + 12x^2 - 3x - 4)<br />= 3x^3 - 2x^2 + 4x - 8 - 5x^3 - 12x^2 + 3x + 4.<br />\]<br /><br />### Step 2: Combine like terms<br />Now, group the terms with the same powers of \(x\):<br /><br />- For \(x^3\): \(3x^3 - 5x^3 = -2x^3\),<br />- For \(x^2\): \(-2x^2 - 12x^2 = -14x^2\),<br />- For \(x^1\): \(4x + 3x = 7x\),<br />- For the constant term: \(-8 + 4 = -4\).<br /><br />Thus, the result is:<br /><br />\[<br />-2x^3 - 14x^2 + 7x - 4.<br />\]<br /><br />### Final Answer:<br />The difference is:<br /><br />\[<br />\boxed{-2x^3 - 14x^2 + 7x - 4}.<br />\]