Question
Subtract. Express your answer as a polynomial in standard form. (1 point)
(8x3−4x2+9x+8)−(6x2−7x+8) =
(8x3−4x2+9x+8)−(6x2−7x+8) =
Answers
GPT-4o mini
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:
\[
\boxed{8x^3 - 10x^2 + 16x}
\]
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:
\[
\boxed{8x^3 - 10x^2 + 16x}
\]