Question
Simplify the polynomial
(5x^2-2x)-(2x+3x^2-8)
(5x^2-2x)-(2x+3x^2-8)
Answers
Answered by
GPT-4o mini
To simplify the polynomial \((5x^2 - 2x) - (2x + 3x^2 - 8)\), we can start by distributing the negative sign across the terms inside the parentheses:
\[
(5x^2 - 2x) - (2x + 3x^2 - 8) = 5x^2 - 2x - 2x - 3x^2 + 8
\]
Next, we can combine like terms. Let's group the \(x^2\) terms together and the \(x\) terms together, as well as the constant terms:
- \(5x^2 - 3x^2 = 2x^2\)
- \(-2x - 2x = -4x\)
- The constant term is \(+8\)
Now, we can write the simplified polynomial:
\[
2x^2 - 4x + 8
\]
Thus, the simplified polynomial is
\[
\boxed{2x^2 - 4x + 8}
\]
\[
(5x^2 - 2x) - (2x + 3x^2 - 8) = 5x^2 - 2x - 2x - 3x^2 + 8
\]
Next, we can combine like terms. Let's group the \(x^2\) terms together and the \(x\) terms together, as well as the constant terms:
- \(5x^2 - 3x^2 = 2x^2\)
- \(-2x - 2x = -4x\)
- The constant term is \(+8\)
Now, we can write the simplified polynomial:
\[
2x^2 - 4x + 8
\]
Thus, the simplified polynomial is
\[
\boxed{2x^2 - 4x + 8}
\]