Question
Step 3: Add the like terms identified in Step 2 to simplify the polynomial.
(3x – 5 – 7x2) – (–2 + 6x2 – 5x)
(3x – 5 – 7x2) – (–2 + 6x2 – 5x)
Answers
GPT-4o mini
To simplify the given polynomial expression:
\[
(3x - 5 - 7x^2) - (-2 + 6x^2 - 5x)
\]
we need to first distribute the negative sign across the second polynomial:
\[
(3x - 5 - 7x^2) + (2 - 6x^2 + 5x)
\]
Now, we can combine like terms. First, let's group the terms by their degrees:
- For \(x^2\) terms: \(-7x^2 + (-6x^2) = -7x^2 - 6x^2 = -13x^2\)
- For \(x\) terms: \(3x + 5x = 8x\)
- For constant terms: \(-5 + 2 = -3\)
Putting it all together, we combine the results:
\[
-13x^2 + 8x - 3
\]
Thus, the simplified form of the polynomial is:
\[
-13x^2 + 8x - 3
\]
\[
(3x - 5 - 7x^2) - (-2 + 6x^2 - 5x)
\]
we need to first distribute the negative sign across the second polynomial:
\[
(3x - 5 - 7x^2) + (2 - 6x^2 + 5x)
\]
Now, we can combine like terms. First, let's group the terms by their degrees:
- For \(x^2\) terms: \(-7x^2 + (-6x^2) = -7x^2 - 6x^2 = -13x^2\)
- For \(x\) terms: \(3x + 5x = 8x\)
- For constant terms: \(-5 + 2 = -3\)
Putting it all together, we combine the results:
\[
-13x^2 + 8x - 3
\]
Thus, the simplified form of the polynomial is:
\[
-13x^2 + 8x - 3
\]