Question

1. what does the term $3x \cdot 2x$ produce in the area model?

a. $6x^2$

b. $6x$

c. $x^2$

d. $5x^2$

Explanation:

Step1: Recall multiplication of coefficients and variables

When multiplying \(3x\) and \(2x\), we multiply the coefficients (the numbers) and the variables (the \(x\) terms) separately. For the coefficients: \(3\times2 = 6\). For the variables: \(x\times x=x^{2}\) (using the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\), here \(m = 1\) and \(n = 1\), so \(x^{1}\times x^{1}=x^{1+1}=x^{2}\)).

Step2: Combine the results

Multiply the results from the coefficients and the variables together: \(6\times x^{2}=6x^{2}\).

Answer:

a. \(6x^{2}\)