Question

determine the product of three linear factors. verify graphically that the expressions are equivalent.
sample problem
$3x(x + 3)(x - 2)$
$= 3x(x^2 - 2x + 3x - 6)$
$= 3x(x^2 + x - 6)$
$= 3x^3 + 3x^2 - 18x$
the graph of the original expression and the graph of the final expression are the same. so the expressions are equivalent.
$\left(\frac{1}{2}x\
ight)\left(\frac{2}{3}x\
ight)\left(\frac{1}{4}x - 1\
ight) = \square$
type the answer in the space provided. use numbers instead of words.

Explanation:

Step1: Multiply the constant terms

$\frac{1}{2} \times \frac{2}{3} \times \frac{1}{4} = \frac{1 \times 2 \times 1}{2 \times 3 \times 4} = \frac{2}{24} = \frac{1}{12}$

Step2: Multiply the $x$ terms

$x \times x \times x = x^3$

Step3: Multiply the constant with $x^3$

$\frac{1}{12}x^3$

Step4: Multiply constants with the linear term

$\frac{1}{2} \times \frac{2}{3} \times (-1) = -\frac{1}{3}$

Step5: Combine all terms

$\frac{1}{12}x^3 - \frac{1}{3}x^2$

Answer:

$\frac{1}{12}x^3 - \frac{1}{3}x^2$