After applying the distributive property to 3d(4 - 6e), the correct expression is 3d(4 - 6e) = 12d - 18de. The original statement is false because it incorrectly lists the term as +18e instead of -18de.
The question involves applying the distributive property of multiplication over subtraction in algebra.
The distributive property states that a(b + c) = ab + ac.
So, to apply the distributive property to 3d(4 - 6e), you multiply 3d by each term inside the parentheses separately:
3d * 4 = 12d and 3d * (-6e) = -18de.
Therefore, the correct expression after applying the distributive property is:
3d(4 - 6e) = 12d - 18de.
The initial statement given in the question, 3d(4 - 6e) = 12d + 18e, is incorrect because the sign in front of 18e should be negative, as it results from multiplying a positive number (3d) with a negative number (-6e).