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Answer :
Sure! Let's multiply the two polynomials step by step.
We have the following expressions to multiply:
[tex]\[
(x^2 - 5x)(2x^2 + x - 3)
\][/tex]
To multiply them, we'll distribute each term in the first polynomial across all terms in the second polynomial.
1. First, distribute [tex]\(x^2\)[/tex]:
- [tex]\(x^2 \cdot 2x^2 = 2x^4\)[/tex]
- [tex]\(x^2 \cdot x = x^3\)[/tex]
- [tex]\(x^2 \cdot -3 = -3x^2\)[/tex]
2. Then, distribute [tex]\(-5x\)[/tex]:
- [tex]\(-5x \cdot 2x^2 = -10x^3\)[/tex]
- [tex]\(-5x \cdot x = -5x^2\)[/tex]
- [tex]\(-5x \cdot -3 = 15x\)[/tex]
Now, let's combine all these results:
- [tex]\(2x^4\)[/tex] (from [tex]\(x^2 \cdot 2x^2\)[/tex])
- [tex]\(x^3 - 10x^3 = -9x^3\)[/tex]
- [tex]\(-3x^2 - 5x^2 = -8x^2\)[/tex]
- [tex]\(15x\)[/tex] (from [tex]\(-5x \cdot -3\)[/tex])
Putting it all together, we get:
[tex]\[
2x^4 - 9x^3 - 8x^2 + 15x
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{2x^4 - 9x^3 - 8x^2 + 15x}
\][/tex]
The corresponding answer choice is option D.
We have the following expressions to multiply:
[tex]\[
(x^2 - 5x)(2x^2 + x - 3)
\][/tex]
To multiply them, we'll distribute each term in the first polynomial across all terms in the second polynomial.
1. First, distribute [tex]\(x^2\)[/tex]:
- [tex]\(x^2 \cdot 2x^2 = 2x^4\)[/tex]
- [tex]\(x^2 \cdot x = x^3\)[/tex]
- [tex]\(x^2 \cdot -3 = -3x^2\)[/tex]
2. Then, distribute [tex]\(-5x\)[/tex]:
- [tex]\(-5x \cdot 2x^2 = -10x^3\)[/tex]
- [tex]\(-5x \cdot x = -5x^2\)[/tex]
- [tex]\(-5x \cdot -3 = 15x\)[/tex]
Now, let's combine all these results:
- [tex]\(2x^4\)[/tex] (from [tex]\(x^2 \cdot 2x^2\)[/tex])
- [tex]\(x^3 - 10x^3 = -9x^3\)[/tex]
- [tex]\(-3x^2 - 5x^2 = -8x^2\)[/tex]
- [tex]\(15x\)[/tex] (from [tex]\(-5x \cdot -3\)[/tex])
Putting it all together, we get:
[tex]\[
2x^4 - 9x^3 - 8x^2 + 15x
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{2x^4 - 9x^3 - 8x^2 + 15x}
\][/tex]
The corresponding answer choice is option D.
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