To multiply the linear expressions [tex]\(5.4x\)[/tex] and [tex]\(2x\)[/tex], we should follow these steps:
1. Multiply the coefficients: The coefficients are the numerical parts of each term. Here, the coefficients are [tex]\(5.4\)[/tex] and [tex]\(2\)[/tex]. When we multiply these coefficients together, [tex]\(5.4 \times 2 = 10.8\)[/tex].
2. Add the exponents of [tex]\(x\)[/tex]: In the given expressions, both [tex]\(5.4x\)[/tex] and [tex]\(2x\)[/tex] have [tex]\(x\)[/tex] raised to the first power (i.e., [tex]\(x^1\)[/tex]). When multiplying expressions with the same base, we add the exponents. So, [tex]\(x^1 \times x^1 = x^{1+1} = x^2\)[/tex].
Combining these two results, the product of [tex]\(5.4x\)[/tex] and [tex]\(2x\)[/tex] is:
[tex]\[ 10.8x^2 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{10.8x^2} \][/tex]
