How many terms are \( \begin{array}{l}3 a b-3 b-a+6 \\ 5(3 t+s)-2 t^{2} \\ (9 z+6 x)(3 x-2 z\end{array} \)
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Let’s break down each expression to find the number of terms: 1. In the expression \( 3ab - 3b - a + 6 \), there are four distinct terms: \( 3ab \), \( -3b \), \( -a \), and \( 6 \). 2. For the expression \( 5(3t + s) - 2t^{2} \), when we distribute the 5, we get \( 15t + 5s - 2t^{2} \). This gives us three terms: \( 15t \), \( 5s \), and \( -2t^{2} \). 3. In the expression \( (9z + 6x)(3x - 2z) \), we need to distribute to find the terms: - \( 9z \cdot 3x = 27zx \) - \( 9z \cdot -2z = -18z^2 \) - \( 6x \cdot 3x = 18x^2 \) - \( 6x \cdot -2z = -12zx \) Combining the terms results in \( 27zx - 12zx - 18z^2 + 18x^2 \), which simplifies to \( 15zx - 18z^2 + 18x^2 \). There are three distinct terms here. Adding them all together, the total number of terms is \( 4 + 3 + 3 = 10 \). So, in total, there are **10 terms** in the provided expressions.