$$ (x-6)\left(x^{2}+4 x\right) $$ A. $$ x^{3}-2 x^{2}-24 x $$ B. $$ x^{3}-10 x^{2}-24 x $$ C. $$ x^{3}-2 x^{2}-24 $$ D. $$ x^{3}-10 x^{2}-24 $$

Question

UpStudy AI · Accepted Answer

To expand the expression $$(x - 6)(x^2 + 4x)$$, follow these steps:

1. **Distribute each term in the first polynomial to each term in the second polynomial:**

$$
   (x - 6)(x^2 + 4x) = x \cdot x^2 + x \cdot 4x - 6 \cdot x^2 - 6 \cdot 4x
   $$

2. **Multiply the terms:**

$$
   = x^3 + 4x^2 - 6x^2 - 24x
   $$

3. **Combine like terms:**

$$
   = x^3 + (4x^2 - 6x^2) - 24x
   $$
   
   $$
   = x^3 - 2x^2 - 24x
   $$

So, the correct expanded form is:

**A. $$ x^{3} - 2x^{2} - 24x $$**

Answer: A
The expanded form is $$ x^{3} - 2x^{2} - 24x $$, so the correct answer is A.

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