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:

\[
\boxed{7x^4 - x^3 - 15x^2}
\]
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