91Ó°ÊÓ

First, we need to multiply the complex numbers \((1+3i)(2-7i)\). Apply the distributive property (FOIL method): \[(1+3i)(2-7i) = (1)(2) + (1)(-7i) + (3i)(2) + (3i)(-7i)\] Now simplify the expression: \(= 2 - 7i + 6i - 21i^{2}\) Remember that \(i^2 = -1\), so replace \(i^2\) with \(-1\): \(= 2 - 7i + 6i + 21\) Combine like terms: \(= 23 - i\)

Now, we will multiply the binomials \((x+3)(2x-7)\). Apply the distributive property (FOIL method): \[(x+3)(2x-7) = (x)(2x) + (x)(-7) + (3)(2x) + (3)(-7)\] Now simplify the expression: \(= 2x^2 - 7x + 6x - 21\) Combine like terms: \(= 2x^2 - x - 21\)

Comparing the multiplication of the complex numbers \((1+3i)(2-7i)\) and the binomials \((x+3)(2x-7)\), we can see that the process is very similar. In both cases, we used the distributive property (FOIL method) to expand the expressions and then combined like terms. Notice that while distributing and combining terms, the process remains the same for both. The only difference is that in complex number multiplication, we have an imaginary unit (i) while in binomial multiplication, we do not. Other than that, the process of multiplication is essentially identical. So, multiplying \((1+3i)(2-7i)\) is conceptually similar to multiplying \((x+3)(2x-7)\), as both involve distributing terms and combining like terms.