Question

1. factor: $0.008x^{3}-\frac{1}{125}$.a. $(0.2x+\frac{1}{5})(0.04x^{2}-0.04x+\frac{1}{25})$b. $(0.2x+\frac{1}{5})(0.04x^{2}+0.04x-\frac{1}{625})$c. $(0.2x-\frac{1}{5})(0.04x^{2}-0.04x-\frac{1}{625})$d. $(0.2x-\frac{1}{5})(0.04x^{2}+0.04x+\frac{1}{25})$

Explanation:

Step1: Recognize difference of cubes

$0.008x^3 = (0.2x)^3$, $\frac{1}{125} = (\frac{1}{5})^3$

Step2: Apply difference of cubes formula

Use $a^3 - b^3 = (a-b)(a^2+ab+b^2)$

Step3: Substitute $a=0.2x$, $b=\frac{1}{5}$

$(0.2x)^3 - (\frac{1}{5})^3 = (0.2x - \frac{1}{5})[(0.2x)^2 + (0.2x)(\frac{1}{5}) + (\frac{1}{5})^2]$

Step4: Simplify the quadratic term

$(0.2x)^2=0.04x^2$, $(0.2x)(\frac{1}{5})=0.04x$, $(\frac{1}{5})^2=\frac{1}{25}$
Result: $(0.2x - \frac{1}{5})(0.04x^{2} + 0.04x + \frac{1}{25})$

Answer:

d. $(0.2x - \frac{1}{5})(0.04x^{2} + 0.04x + \frac{1}{25})$