Question

factor completely: $b^3 - 1000$
a $(b - 10)(b^2 + 5b - 10)$
b $(b - 10)(b^2 + 10b + 100)$
c $(b - 10)^3$
d $(b - 10)(b + 10)^2$

Explanation:

Step1: Recall the difference of cubes formula

The formula for factoring the difference of cubes is \(a^3 - b^3=(a - b)(a^2+ab + b^2)\).

Step2: Identify \(a\) and \(b\) in the given expression

In the expression \(b^3-1000\), we can rewrite \(1000\) as \(10^3\). So, \(a = b\) and \(b = 10\) (using the difference of cubes formula notation).

Step3: Apply the difference of cubes formula

Substitute \(a = b\) and \(b = 10\) into the formula \(a^3 - b^3=(a - b)(a^2+ab + b^2)\). We get:
\(b^3-10^3=(b - 10)(b^2+(b)(10)+10^2)=(b - 10)(b^2 + 10b+100)\)

Answer:

B. \((b - 10)(b^2 + 10b + 100)\)