Answer :
Sure! Let's work through the multiplication of the monomials step-by-step:
We have two monomials to multiply: [tex]\(3x^2\)[/tex] and [tex]\(4x^3\)[/tex].
1. Multiply the coefficients:
- The coefficients are the numbers in front of the variables. In this case, they are 3 and 4.
- Multiply these coefficients: [tex]\(3 \times 4 = 12\)[/tex].
2. Add the exponents of the variable [tex]\(x\)[/tex]:
- For the variable [tex]\(x\)[/tex], we have the exponents 2 and 3 from [tex]\(x^2\)[/tex] and [tex]\(x^3\)[/tex], respectively.
- When multiplying like bases, you add the exponents: [tex]\(2 + 3 = 5\)[/tex].
3. Form the resulting monomial:
- Combine the result from the coefficients and the new exponent for [tex]\(x\)[/tex].
- This gives us: [tex]\(12x^5\)[/tex].
So, the product of [tex]\((3x^2) \times (4x^3)\)[/tex] is [tex]\(12x^5\)[/tex].
Therefore, the answer is C) [tex]\(12x^5\)[/tex].
We have two monomials to multiply: [tex]\(3x^2\)[/tex] and [tex]\(4x^3\)[/tex].
1. Multiply the coefficients:
- The coefficients are the numbers in front of the variables. In this case, they are 3 and 4.
- Multiply these coefficients: [tex]\(3 \times 4 = 12\)[/tex].
2. Add the exponents of the variable [tex]\(x\)[/tex]:
- For the variable [tex]\(x\)[/tex], we have the exponents 2 and 3 from [tex]\(x^2\)[/tex] and [tex]\(x^3\)[/tex], respectively.
- When multiplying like bases, you add the exponents: [tex]\(2 + 3 = 5\)[/tex].
3. Form the resulting monomial:
- Combine the result from the coefficients and the new exponent for [tex]\(x\)[/tex].
- This gives us: [tex]\(12x^5\)[/tex].
So, the product of [tex]\((3x^2) \times (4x^3)\)[/tex] is [tex]\(12x^5\)[/tex].
Therefore, the answer is C) [tex]\(12x^5\)[/tex].
