Question

Simplify the expression (3x^3-2)(x^2+4)

A: 3x^5+12x^3-2x^2-8

B:13x^10-8

C 3x^6+12x^3-2x^2-8

D: 3x^+10x-8

Answer 1

To simplify the expression \((3x^3 - 2)(x^2 + 4)\), we will use the distributive property (also known as the FOIL method for binomials).

1. Distribute \(3x^3\) to both terms in the second polynomial:
\[
3x^3 \cdot x^2 = 3x^5
\]
\[
3x^3 \cdot 4 = 12x^3
\]

2. Distribute \(-2\) to both terms in the second polynomial:
\[
-2 \cdot x^2 = -2x^2
\]
\[
-2 \cdot 4 = -8
\]

Now, combine all the terms together:
\[
3x^5 + 12x^3 - 2x^2 - 8
\]

Thus, the simplified expression is:
\[
3x^5 + 12x^3 - 2x^2 - 8
\]

Looking at the options provided, we see that this is equivalent to option **A**.

So the final answer is:
**A: \(3x^5 + 12x^3 - 2x^2 - 8\)**