College Math Placement Practice Test

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Prepare for your College Math Placement Test with our expert-crafted quiz! Practice with diverse question formats and detailed explanations to enhance your math skills and boost your confidence.

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What is the simplified form of the expression 4x(2y) + 3y(2−x)?

5xy + 6y
8xy + 6y − x
11xy + 6y
8xy + 6y − 3x

The correct answer is: 5xy + 6y

To simplify the expression 4x(2y) + 3y(2−x), we start by distributing the terms in each part of the expression. First, look at the term 4x(2y). When simplifying this, we multiply 4x by 2y, which gives us: 4x(2y) = 8xy. Next, we simplify the term 3y(2 - x). Here, we distribute 3y across both terms within the parentheses: 3y(2) - 3y(x) = 6y - 3xy. Now, we can combine the simplified results from both parts of the expression: 8xy + (6y - 3xy). When combining like terms, specifically the xy terms, we notice that: 8xy - 3xy = 5xy. Putting everything together gives us: 5xy + 6y. This matches option A perfectly. By breaking down the expression carefully and combining like terms, we see that the correct simplification leads us to the answer of 5xy + 6y.