Asked by d
Simplify: (6x^3 -7x^2) - (7x^3 + 8x^2 - 7x^4)
Answers
Answered by
GPT-4o mini
To simplify the expression \((6x^3 - 7x^2) - (7x^3 + 8x^2 - 7x^4)\), we first distribute the negative sign across the second polynomial:
\[
(6x^3 - 7x^2) - (7x^3 + 8x^2 - 7x^4) = 6x^3 - 7x^2 - 7x^3 - 8x^2 + 7x^4
\]
Next, we can combine like terms. Let's reorder the expression:
\[
7x^4 + (6x^3 - 7x^3) + (-7x^2 - 8x^2)
\]
Now, simplify the coefficients for each term:
- For \(x^4\): \(7x^4\)
- For \(x^3\): \(6x^3 - 7x^3 = -1x^3 = -x^3\)
- For \(x^2\): \(-7x^2 - 8x^2 = -15x^2\)
Putting it all together, we have:
\[
7x^4 - x^3 - 15x^2
\]
Thus, the simplified expression is:
\[
\boxed{7x^4 - x^3 - 15x^2}
\]
\[
(6x^3 - 7x^2) - (7x^3 + 8x^2 - 7x^4) = 6x^3 - 7x^2 - 7x^3 - 8x^2 + 7x^4
\]
Next, we can combine like terms. Let's reorder the expression:
\[
7x^4 + (6x^3 - 7x^3) + (-7x^2 - 8x^2)
\]
Now, simplify the coefficients for each term:
- For \(x^4\): \(7x^4\)
- For \(x^3\): \(6x^3 - 7x^3 = -1x^3 = -x^3\)
- For \(x^2\): \(-7x^2 - 8x^2 = -15x^2\)
Putting it all together, we have:
\[
7x^4 - x^3 - 15x^2
\]
Thus, the simplified expression is:
\[
\boxed{7x^4 - x^3 - 15x^2}
\]
There are no human answers yet. A form for humans to post answers is coming very soon!