The error in the work shown lies in the incorrect factoring of the sum \( 18 + 30 \).
To find an equivalent expression for \( 18 + 30 \), we need to correctly identify how to express it in factored form:
- The original expression is \( 18 + 30 \), which simplifies to \( 48 \).
- The next step attempted was to factor this expression, but the factoring shown, \( 6(3 + 10) \), is incorrect for two reasons:
- If you distribute \( 6(3 + 10) \), it gives \( 6 \cdot 3 + 6 \cdot 10 = 18 + 60 \), not \( 48 \).
- Additionally, \( 3 + 10 = 13 \), so \( 6(3 + 10) = 6 \cdot 13 = 78\), which is also incorrect.
Thus, the error occurs in the assumption that \( 18 + 30 \) can be factored as \( 6(3 + 10) \), as that expression does not equate back to the original sum.
A correct way to express \( 18 + 30 \) in a factored form could be \( 6(8) \), since \( 48 = 6 \times 8\).
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