Subtract. Express your answer as a polynomial in standard form. (1 point)

Question

(8x3−4x2+9x+8)−(6x2−7x+8) =

Answer 1

To subtract the polynomials \((8x^3 - 4x^2 + 9x + 8)\) and \((6x^2 - 7x + 8)\), we follow these steps:

1. Distribute the negative sign across the second polynomial: \[ (8x^3 - 4x^2 + 9x + 8) - (6x^2 - 7x + 8) = 8x^3 - 4x^2 + 9x + 8 - 6x^2 + 7x - 8 \]

2. Combine like terms:

   • The \(x^3\) term: \(8x^3\)
   • The \(x^2\) terms: \(-4x^2 - 6x^2 = -10x^2\)
   • The \(x\) terms: \(9x + 7x = 16x\)
   • The constant terms: \(8 - 8 = 0\)

Putting it all together, we get: \[ 8x^3 - 10x^2 + 16x \]

Thus, the answer in standard form is: \[ \boxed{8x^3 - 10x^2 + 16x} \]