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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

1 answer

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: \(3x^5 + 12x^3 - 2x^2 - 8\)