Question

simplify the polynomial by combining like terms.\\(\frac{4}{5}x^{2} - \frac{1}{2}x^{3} + x^{2} - \frac{1}{3}x^{3} + 7\\)\\(\frac{4}{5}x^{2} - \frac{1}{2}x^{3} + x^{2} - \frac{1}{3}x^{3} + 7 = square\\)\\(\text{(simplify your answer. use integers or fractions for any numbers in the expression.)}\\)

Explanation:

Step1: Combine \(x^2\) terms

Identify like terms for \(x^2\): \(\frac{4}{5}x^2\) and \(x^2\). Convert \(x^2\) to \(\frac{5}{5}x^2\) to have a common denominator. Then add: \(\frac{4}{5}x^2+\frac{5}{5}x^2 = \frac{4 + 5}{5}x^2=\frac{9}{5}x^2\).

Step2: Combine \(x^3\) terms

Identify like terms for \(x^3\): \(-\frac{1}{2}x^3\) and \(-\frac{1}{3}x^3\). Find a common denominator (6) and add: \(-\frac{3}{6}x^3-\frac{2}{6}x^3=\frac{-3 - 2}{6}x^3=-\frac{5}{6}x^3\).

Step3: Combine constant and simplified terms

The constant term is 7. Combine all simplified terms: \(-\frac{5}{6}x^3+\frac{9}{5}x^2 + 7\).

Answer:

\(-\frac{5}{6}x^3+\frac{9}{5}x^2 + 7\)