Question: b -7x^2(1 - x)^3
1. **State the problem:** Simplify or expand the expression $$b -7x^2(1 - x)^3$$.
2. **Recall the binomial expansion formula:** For any binomial $$(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$$.
3. **Apply the formula to** $$(1 - x)^3$$:
$$
(1 - x)^3 = 1^3 - 3 \cdot 1^2 \cdot x + 3 \cdot 1 \cdot x^2 - x^3 = 1 - 3x + 3x^2 - x^3
$$
4. **Multiply the result by** $$-7x^2$$:
$$
-7x^2(1 - 3x + 3x^2 - x^3) = -7x^2 + 21x^3 - 21x^4 + 7x^5
$$
5. **Combine with** $$b$$:
$$
b - 7x^2 + 21x^3 - 21x^4 + 7x^5
$$
6. **Final simplified expression:**
$$
b - 7x^2 + 21x^3 - 21x^4 + 7x^5
$$
This is the expanded form of the original expression.