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Simplify [tex]\left(3 x^2\right)\left(4 x^3\right)[/tex].

A. [tex]12 x^5[/tex]
B. [tex]7 x^5[/tex]
C. [tex]7 x^6[/tex]
D. [tex]12 x^6[/tex]

Answer :

Sure, let's simplify the expression [tex]\((3x^2)(4x^3)\)[/tex].

1. Multiply the Coefficients:
- First, identify the numerical coefficients in each expression. Here, we have 3 and 4.
- Multiply these coefficients: [tex]\(3 \times 4 = 12\)[/tex].

2. Add the Exponents of [tex]\(x\)[/tex]:
- Next, look at the powers of [tex]\(x\)[/tex] in each part of the expression. We have [tex]\(x^2\)[/tex] and [tex]\(x^3\)[/tex].
- When multiplying expressions with the same base, you add the exponents: [tex]\(2 + 3 = 5\)[/tex].

3. Combine the Results:
- Now, combine the simplified coefficient and the power of [tex]\(x\)[/tex]: [tex]\(12x^5\)[/tex].

So, the simplified expression is [tex]\(12x^5\)[/tex].

The correct choice from the options given is [tex]\(\boxed{12x^5}\)[/tex].

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