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Multiply the following expression:

[tex](4x^2 + 7x)(5x^2 - 3x)[/tex]

Choose the correct option:

A. [tex]20x^4 + 35x^3 - 21x^2[/tex]

B. [tex]20x^4 + 23x^3 - 21x^2[/tex]

C. [tex]20x^4 + 35x^2 - 21x[/tex]

D. [tex]20x^4 + 23x^2 - 21x[/tex]

Answer :

To solve the problem, we need to multiply the two polynomials: [tex]\((4x^2 + 7x)\)[/tex] and [tex]\((5x^2 - 3x)\)[/tex].

Here’s how you can do it step-by-step:

1. Multiply each term in the first polynomial by each term in the second polynomial:
- Multiply [tex]\(4x^2\)[/tex] by [tex]\(5x^2\)[/tex]:
[tex]\[
4x^2 \cdot 5x^2 = 20x^4
\][/tex]

- Multiply [tex]\(4x^2\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
4x^2 \cdot (-3x) = -12x^3
\][/tex]

- Multiply [tex]\(7x\)[/tex] by [tex]\(5x^2\)[/tex]:
[tex]\[
7x \cdot 5x^2 = 35x^3
\][/tex]

- Multiply [tex]\(7x\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
7x \cdot (-3x) = -21x^2
\][/tex]

2. Combine all of the results:
- From the above multiplication you have:
[tex]\[
20x^4 - 12x^3 + 35x^3 - 21x^2
\][/tex]

3. Simplify by combining like terms:
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-12x^3 + 35x^3 = 23x^3
\][/tex]

4. Write the final expression:
- Combine all the terms to get:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]

This matches the answer choice B: [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].

Thanks for taking the time to read Multiply the following expression tex 4x 2 7x 5x 2 3x tex Choose the correct option A tex 20x 4 35x 3 21x 2 tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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