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Answer :
Sure, let's go through the multiplication step-by-step.
We need to multiply the expressions [tex]\((x^2 - 5x)\)[/tex] and [tex]\((2x^2 + x - 3)\)[/tex].
1. Distribute [tex]\(x^2\)[/tex] through [tex]\((2x^2 + x - 3)\)[/tex]:
- [tex]\(x^2 \times 2x^2 = 2x^4\)[/tex]
- [tex]\(x^2 \times x = x^3\)[/tex]
- [tex]\(x^2 \times -3 = -3x^2\)[/tex]
So, the result of distributing [tex]\(x^2\)[/tex] is [tex]\(2x^4 + x^3 - 3x^2\)[/tex].
2. Distribute [tex]\(-5x\)[/tex] through [tex]\((2x^2 + x - 3)\)[/tex]:
- [tex]\((-5x) \times 2x^2 = -10x^3\)[/tex]
- [tex]\((-5x) \times x = -5x^2\)[/tex]
- [tex]\((-5x) \times -3 = +15x\)[/tex]
So, the result of distributing [tex]\(-5x\)[/tex] is [tex]\(-10x^3 - 5x^2 + 15x\)[/tex].
3. Combine all the terms:
- [tex]\(2x^4\)[/tex] (no like terms, so it stays as [tex]\(2x^4\)[/tex])
- [tex]\(x^3 - 10x^3 = -9x^3\)[/tex]
- [tex]\(-3x^2 - 5x^2 = -8x^2\)[/tex]
- [tex]\(15x\)[/tex] (no like terms, so it stays as [tex]\(15x\)[/tex])
Combining everything, we get the final result:
[tex]\[
2x^4 - 9x^3 - 8x^2 + 15x
\][/tex]
So the correct answer is A. [tex]\(2x^4 - 9x^3 - 8x^2 + 15x\)[/tex].
We need to multiply the expressions [tex]\((x^2 - 5x)\)[/tex] and [tex]\((2x^2 + x - 3)\)[/tex].
1. Distribute [tex]\(x^2\)[/tex] through [tex]\((2x^2 + x - 3)\)[/tex]:
- [tex]\(x^2 \times 2x^2 = 2x^4\)[/tex]
- [tex]\(x^2 \times x = x^3\)[/tex]
- [tex]\(x^2 \times -3 = -3x^2\)[/tex]
So, the result of distributing [tex]\(x^2\)[/tex] is [tex]\(2x^4 + x^3 - 3x^2\)[/tex].
2. Distribute [tex]\(-5x\)[/tex] through [tex]\((2x^2 + x - 3)\)[/tex]:
- [tex]\((-5x) \times 2x^2 = -10x^3\)[/tex]
- [tex]\((-5x) \times x = -5x^2\)[/tex]
- [tex]\((-5x) \times -3 = +15x\)[/tex]
So, the result of distributing [tex]\(-5x\)[/tex] is [tex]\(-10x^3 - 5x^2 + 15x\)[/tex].
3. Combine all the terms:
- [tex]\(2x^4\)[/tex] (no like terms, so it stays as [tex]\(2x^4\)[/tex])
- [tex]\(x^3 - 10x^3 = -9x^3\)[/tex]
- [tex]\(-3x^2 - 5x^2 = -8x^2\)[/tex]
- [tex]\(15x\)[/tex] (no like terms, so it stays as [tex]\(15x\)[/tex])
Combining everything, we get the final result:
[tex]\[
2x^4 - 9x^3 - 8x^2 + 15x
\][/tex]
So the correct answer is A. [tex]\(2x^4 - 9x^3 - 8x^2 + 15x\)[/tex].
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