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Answer :
Sure! Let's multiply the given polynomials step-by-step.
We need to multiply two polynomial expressions: [tex]\((x^2 - 5x)\)[/tex] and [tex]\((2x^2 + x - 3)\)[/tex].
We'll use the distributive property (often referred to as the FOIL method for binomials) to expand this expression:
Step 1: Multiply [tex]\(x^2\)[/tex] with every term in the second polynomial:
- [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]
Step 2: Multiply [tex]\(-5x\)[/tex] with every term in the second polynomial:
- [tex]\(-5x \times 2x^2 = -10x^3\)[/tex]
- [tex]\(-5x \times x = -5x^2\)[/tex]
- [tex]\(-5x \times -3 = 15x\)[/tex]
Step 3: Now, combine all these terms:
- [tex]\(2x^4\)[/tex]
- [tex]\(x^3 - 10x^3 = -9x^3\)[/tex]
- [tex]\(-3x^2 - 5x^2 = -8x^2\)[/tex]
- [tex]\(15x\)[/tex]
So, the expanded expression is:
[tex]\[2x^4 - 9x^3 - 8x^2 + 15x\][/tex]
The option that matches this result is C. [tex]\(2x^4 - 9x^3 - 8x^2 + 15x\)[/tex].
We need to multiply two polynomial expressions: [tex]\((x^2 - 5x)\)[/tex] and [tex]\((2x^2 + x - 3)\)[/tex].
We'll use the distributive property (often referred to as the FOIL method for binomials) to expand this expression:
Step 1: Multiply [tex]\(x^2\)[/tex] with every term in the second polynomial:
- [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]
Step 2: Multiply [tex]\(-5x\)[/tex] with every term in the second polynomial:
- [tex]\(-5x \times 2x^2 = -10x^3\)[/tex]
- [tex]\(-5x \times x = -5x^2\)[/tex]
- [tex]\(-5x \times -3 = 15x\)[/tex]
Step 3: Now, combine all these terms:
- [tex]\(2x^4\)[/tex]
- [tex]\(x^3 - 10x^3 = -9x^3\)[/tex]
- [tex]\(-3x^2 - 5x^2 = -8x^2\)[/tex]
- [tex]\(15x\)[/tex]
So, the expanded expression is:
[tex]\[2x^4 - 9x^3 - 8x^2 + 15x\][/tex]
The option that matches this result is C. [tex]\(2x^4 - 9x^3 - 8x^2 + 15x\)[/tex].
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