Divide out any common factors by using the fundamental property. ((1-2r)(1+2r+4r^2))/(3(1+2r+4r^2))

Answer 1

To begin simplifying the expression \(\frac{(1-2r)(1+2r+4r^2)}{3(1+2r+4r^2)}\), we can observe the common factors in the numerator and the denominator.

The expression has the term \((1+2r+4r^2)\) in both the numerator and the denominator. We can use this common factor to simplify the expression:

1. Identify the common factor: \[ 1 + 2r + 4r^2 \]

2. Cancel the common factor from both the numerator and the denominator: \[ \frac{(1-2r)\cancel{(1+2r+4r^2)}}{3\cancel{(1+2r+4r^2)}} = \frac{1 - 2r}{3} \]

Thus, the simplified expression is: \[ \frac{1 - 2r}{3} \]