High School

Multiply the following expression:

[tex]\[(x^2 - 5x)(2x^2 + x - 3)\][/tex]

Choose the correct answer:

A. [tex]\[2x^4 - 9x^3 - 8x^2 + 15x\][/tex]

B. [tex]\[4x^4 + 9x^3 - 8x^2 + 15x\][/tex]

C. [tex]\[2x^4 + 9x^3 - 8x^2 + 15x\][/tex]

D. [tex]\[2x^4 - 9x^3 - 9x^2 - 15x\][/tex]

Answer :

Sure! Let's multiply the expressions [tex]\((x^2 - 5x)\)[/tex] and [tex]\((2x^2 + x - 3)\)[/tex] step by step.

1. Distribute each term of the first polynomial [tex]\((x^2 - 5x)\)[/tex] with every term of the second polynomial [tex]\((2x^2 + x - 3)\)[/tex].

- Multiply [tex]\(x^2\)[/tex] by each 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]

- Multiply [tex]\(-5x\)[/tex] by each 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]

2. Combine the results from each distribution step:

[tex]\[2x^4 + x^3 - 3x^2 - 10x^3 - 5x^2 + 15x\][/tex]

3. Combine like terms:

- [tex]\(x^3 - 10x^3\)[/tex] results in [tex]\(-9x^3\)[/tex]
- [tex]\(-3x^2 - 5x^2\)[/tex] combines to [tex]\(-8x^2\)[/tex]

So, the expression simplifies to:

[tex]\[2x^4 - 9x^3 - 8x^2 + 15x\][/tex]

Thus, the correct answer is:
[tex]\[2x^4 - 9x^3 - 8x^2 + 15x\][/tex]

So, the correct choice is A. [tex]\(2x^4 - 9x^3 - 8x^2 + 15x\)[/tex]

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