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Answer :
To solve the given expression [tex]\(3x^8(-2x + 6)\)[/tex], we need to use the distributive property. The distributive property allows us to multiply each term inside the parentheses by the term outside the parentheses. Here’s how you can do it step-by-step:
1. Identify the terms: We have two terms inside the parentheses, [tex]\(-2x\)[/tex] and [tex]\(6\)[/tex]. The term outside the parentheses is [tex]\(3x^8\)[/tex].
2. Distribute the [tex]\(3x^8\)[/tex] to the first term [tex]\(-2x\)[/tex]:
- Multiply the coefficients and combine the powers of [tex]\(x\)[/tex].
- The coefficient part: [tex]\(3 \times -2 = -6\)[/tex].
- The variable part: [tex]\(x^8 \times x = x^{8+1} = x^9\)[/tex].
- So, the product for the first term is [tex]\(-6x^9\)[/tex].
3. Distribute the [tex]\(3x^8\)[/tex] to the second term [tex]\(6\)[/tex]:
- Multiply the coefficients.
- The coefficient part: [tex]\(3 \times 6 = 18\)[/tex].
- The variable part remains [tex]\(x^8\)[/tex] since there's no [tex]\(x\)[/tex] in the number [tex]\(6\)[/tex].
- So, the product for the second term is [tex]\(18x^8\)[/tex].
4. Combine the results: Put the distributed products together.
- From steps 2 and 3, we have [tex]\(-6x^9 + 18x^8\)[/tex].
Therefore, the expanded expression is [tex]\(-6x^9 + 18x^8\)[/tex], which can also be factored or rewritten as [tex]\(6x^8(3 - x)\)[/tex], showing the relationship between the simplified form and the distributed terms.
1. Identify the terms: We have two terms inside the parentheses, [tex]\(-2x\)[/tex] and [tex]\(6\)[/tex]. The term outside the parentheses is [tex]\(3x^8\)[/tex].
2. Distribute the [tex]\(3x^8\)[/tex] to the first term [tex]\(-2x\)[/tex]:
- Multiply the coefficients and combine the powers of [tex]\(x\)[/tex].
- The coefficient part: [tex]\(3 \times -2 = -6\)[/tex].
- The variable part: [tex]\(x^8 \times x = x^{8+1} = x^9\)[/tex].
- So, the product for the first term is [tex]\(-6x^9\)[/tex].
3. Distribute the [tex]\(3x^8\)[/tex] to the second term [tex]\(6\)[/tex]:
- Multiply the coefficients.
- The coefficient part: [tex]\(3 \times 6 = 18\)[/tex].
- The variable part remains [tex]\(x^8\)[/tex] since there's no [tex]\(x\)[/tex] in the number [tex]\(6\)[/tex].
- So, the product for the second term is [tex]\(18x^8\)[/tex].
4. Combine the results: Put the distributed products together.
- From steps 2 and 3, we have [tex]\(-6x^9 + 18x^8\)[/tex].
Therefore, the expanded expression is [tex]\(-6x^9 + 18x^8\)[/tex], which can also be factored or rewritten as [tex]\(6x^8(3 - x)\)[/tex], showing the relationship between the simplified form and the distributed terms.
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