To simplify the expression \(12mn + 30m^2n^3\), we can factor out the common terms from each part of the expression.

Both terms share the common factors \(m\) and \(n\):

1. \(12mn = 12 \cdot m \cdot n\)
2. \(30m^2n^3 = 30 \cdot m \cdot m \cdot n \cdot n \cdot n\)

The greatest common factor (GCF) is \(m \cdot n\).

Let's factor \(mn\) out of the expression:

\[ 12mn + 30m^2n^3 = mn(12 + 30mn^2) \]

Thus, the factored form of the expression is:

\[ 12mn + 30m^2n^3 = mn(12 + 30mn^2) \]

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Learn how to simplify the expression 12mn + 30m²n³ using factorization. This problem involves algebraic concepts such as polynomials and factorization of expressions with variables. Suitable for students in Grades 9-12.

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