Questions: Collect like terms. [ 7 u^9 v-3 u v^2+2 u^9 v-3 u v^2 ]

Solution Steps

To collect like terms, we need to identify terms with the same variables raised to the same powers and then combine their coefficients. In this expression, we have two types of terms: \(u^9 v\) and \(u v^2\). We will sum the coefficients of these like terms separately.

In the expression \(7 u^{9} v - 3 u v^{2} + 2 u^{9} v - 3 u v^{2}\), we identify the like terms. The terms \(7 u^{9} v\) and \(2 u^{9} v\) are like terms, as they both contain \(u^{9} v\). The terms \(-3 u v^{2}\) and \(-3 u v^{2}\) are also like terms, as they both contain \(u v^{2}\).

We combine the coefficients of the like terms:

• For \(u^{9} v\): \(7 + 2 = 9\)
• For \(u v^{2}\): \(-3 - 3 = -6\)

Thus, the expression simplifies to: \[ 9 u^{9} v - 6 u v^{2} \]

Final Answer