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Answer :
Sure! Let's solve the problem step-by-step:
We need to find the product of [tex]\((4x)\)[/tex], [tex]\((-3x^8)\)[/tex], and [tex]\((-7x^3)\)[/tex].
### Step 1: Multiply the Coefficients
First, we'll multiply the numerical coefficients together:
- The coefficients are [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- Multiply them:
[tex]\[
4 \times (-3) \times (-7) = 84
\][/tex]
Note that multiplying two negative numbers [tex]\(-3\)[/tex] and [tex]\(-7\)[/tex] gives a positive product.
### Step 2: Combine the Variables
Now, let's handle the variables:
- We have three factors involving [tex]\(x\)[/tex]: [tex]\(x\)[/tex], [tex]\(x^8\)[/tex], and [tex]\(x^3\)[/tex].
- Use the rule for multiplying powers with the same base: [tex]\(x^a \times x^b = x^{a+b}\)[/tex].
- Combine the exponents:
[tex]\[
x \times x^8 \times x^3 = x^{1+8+3} = x^{12}
\][/tex]
### Final Step: Combine Everything Together
Now, combine the coefficient and the variable part:
- The product is [tex]\(84\)[/tex] (from the coefficients) and [tex]\(x^{12}\)[/tex] (from the exponents).
Thus, the final product is [tex]\(84x^{12}\)[/tex].
So the correct choice is [tex]\(84 x^{12}\)[/tex].
We need to find the product of [tex]\((4x)\)[/tex], [tex]\((-3x^8)\)[/tex], and [tex]\((-7x^3)\)[/tex].
### Step 1: Multiply the Coefficients
First, we'll multiply the numerical coefficients together:
- The coefficients are [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- Multiply them:
[tex]\[
4 \times (-3) \times (-7) = 84
\][/tex]
Note that multiplying two negative numbers [tex]\(-3\)[/tex] and [tex]\(-7\)[/tex] gives a positive product.
### Step 2: Combine the Variables
Now, let's handle the variables:
- We have three factors involving [tex]\(x\)[/tex]: [tex]\(x\)[/tex], [tex]\(x^8\)[/tex], and [tex]\(x^3\)[/tex].
- Use the rule for multiplying powers with the same base: [tex]\(x^a \times x^b = x^{a+b}\)[/tex].
- Combine the exponents:
[tex]\[
x \times x^8 \times x^3 = x^{1+8+3} = x^{12}
\][/tex]
### Final Step: Combine Everything Together
Now, combine the coefficient and the variable part:
- The product is [tex]\(84\)[/tex] (from the coefficients) and [tex]\(x^{12}\)[/tex] (from the exponents).
Thus, the final product is [tex]\(84x^{12}\)[/tex].
So the correct choice is [tex]\(84 x^{12}\)[/tex].
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