Question

simplify.
\\((6x^3 + x^5 + 2x^2 - 7 - 4x) - (3x^2 - 5x + 2 + 5x^5 + 3x^4)\\)

Explanation:

Step1: Distribute the negative sign

To simplify the expression, we first distribute the negative sign to each term inside the second parentheses:
$$(6x^{3}+x^{5}+2x^{2}-7 - 4x)-(3x^{2}-5x + 2+5x^{5}+3x^{4})=6x^{3}+x^{5}+2x^{2}-7 - 4x-3x^{2}+5x - 2-5x^{5}-3x^{4}$$

Step2: Combine like terms for \(x^{5}\) terms

The terms with \(x^{5}\) are \(x^{5}\) and \(- 5x^{5}\). Combining them:
\(x^{5}-5x^{5}=-4x^{5}\)

Step3: Combine like terms for \(x^{4}\) terms

The only term with \(x^{4}\) is \(-3x^{4}\), so it remains as \(-3x^{4}\)

Step4: Combine like terms for \(x^{3}\) terms

The only term with \(x^{3}\) is \(6x^{3}\), so it remains as \(6x^{3}\)

Step5: Combine like terms for \(x^{2}\) terms

The terms with \(x^{2}\) are \(2x^{2}\) and \(-3x^{2}\). Combining them:
\(2x^{2}-3x^{2}=-x^{2}\)

Step6: Combine like terms for \(x\) terms

The terms with \(x\) are \(-4x\) and \(5x\). Combining them:
\(-4x + 5x=x\)

Step7: Combine like terms for constant terms

The constant terms are \(-7\) and \(-2\). Combining them:
\(-7-2=-9\)

Step8: Write the simplified expression in standard form

Now, we combine all the simplified terms in descending order of exponents:
\(-4x^{5}-3x^{4}+6x^{3}-x^{2}+x - 9\)

Answer:

\(-4x^{5}-3x^{4}+6x^{3}-x^{2}+x - 9\)