Question

multiplying with variable expressions
use this explore tool to model and investigate the product of two factors.
to use this tool, drag and drop the variable and number tiles into the horizontal bar at the top. drag and drop the positive or negative number tiles into the vertical bar at the left. then press the multiply button.

use the explore tool to model the multiplication expression (-4(-2x - 3)).
you will need to use the ((-1))-tiles in the vertical section to model this expression.
enter the product.
(8) (x) (+) (12)
use the distributive property over subtraction to rewrite the multiplication expression.
(-4(-2x - 3) = (quad)(-2x) - (quad)(3)
use the explore tool to determine each product.
((-x)(-1) =
(-1)(-1) =

Explanation:

First Sub - Question: \((-x)(-1)\)

Step 1: Recall the rule of multiplying two negative numbers

When multiplying two negative numbers, the result is positive. Also, when multiplying a variable \(x\) with a constant, we multiply the coefficients (and consider the signs) and keep the variable. Here, the coefficient of \(x\) in \(-x\) is \(- 1\), and we are multiplying by \(-1\).
So, \((-x)(-1)=(-1\times - 1)x\)

Step 2: Calculate the product of the coefficients

We know that \(-1\times - 1 = 1\). So, \((-1\times - 1)x=1\times x=x\)

Step 1: Recall the rule of multiplying two negative numbers

The rule for multiplying two negative real numbers is that the product is positive. So, we need to calculate the product of \(-1\) and \(-1\).

Step 2: Calculate the product

\(-1\times - 1 = 1\) (since the product of two negative numbers is positive)

Answer:

\(x\)

Second Sub - Question: \((-1)(-1)\)