To simplify the expression [tex]\((2x)(4y)\)[/tex], follow these steps:
1. Identify the constants and the variables: In the expression [tex]\((2x)(4y)\)[/tex], [tex]\(2\)[/tex] and [tex]\(4\)[/tex] are constants, while [tex]\(x\)[/tex] and [tex]\(y\)[/tex] are variables.
2. Multiply the constants together: Multiply the constants [tex]\(2\)[/tex] and [tex]\(4\)[/tex] to get:
[tex]\[
2 \times 4 = 8
\][/tex]
3. Multiply the variables: Multiply the variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex] to get:
[tex]\[
x \times y = xy
\][/tex]
4. Combine the results: Combine the product of the constants and the product of the variables to get the simplified expression:
[tex]\[
8 \times xy = 8xy
\][/tex]
Therefore, the correct simplification of [tex]\((2x)(4y)\)[/tex] is:
[tex]\[
8xy
\][/tex]
The correct answer is [tex]\(\boxed{8xy}\)[/tex].
