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].
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].
