Question: okay how do i do $x^2(2x-1)^3$
1. **State the problem:** We want to expand or simplify the expression $$x^2(2x-1)^3$$.
2. **Recall the formula:** To expand a binomial raised to a power, use the binomial theorem or expand step-by-step.
3. **Expand $(2x-1)^3$ using the binomial theorem:**
$$ (a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 $$
where $a=2x$ and $b=1$.
4. **Calculate each term:**
$$ (2x)^3 = 8x^3 $$
$$ 3(2x)^2(1) = 3 \times 4x^2 = 12x^2 $$
$$ 3(2x)(1)^2 = 6x $$
$$ 1^3 = 1 $$
5. **Put it all together:**
$$ (2x-1)^3 = 8x^3 - 12x^2 + 6x - 1 $$
6. **Multiply by $x^2$:**
$$ x^2(8x^3 - 12x^2 + 6x - 1) = 8x^{5} - 12x^{4} + 6x^{3} - x^{2} $$
7. **Final answer:**
$$ \boxed{8x^{5} - 12x^{4} + 6x^{3} - x^{2}} $$