High School

We appreciate your visit to Multiply tex left 4x 2 7x right left 5x 2 3x right tex A tex 20x 4 35x 3 21x 2 tex B tex 20x. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Multiply: [tex]\left(4x^2+7x\right)\left(5x^2-3x\right)[/tex]

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 multiply the expressions [tex]\((4x^2 + 7x)\)[/tex] and [tex]\((5x^2 - 3x)\)[/tex], we will use the distributive property, also known as the FOIL method when dealing with binomials.

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

1. Multiply the first terms:
[tex]\[
4x^2 \times 5x^2 = 20x^4
\][/tex]

2. Multiply the outer terms:
[tex]\[
4x^2 \times (-3x) = -12x^3
\][/tex]

3. Multiply the inner terms:
[tex]\[
7x \times 5x^2 = 35x^3
\][/tex]

4. Multiply the last terms:
[tex]\[
7x \times (-3x) = -21x^2
\][/tex]

5. Combine like terms:

Now add all these results together:
[tex]\[
20x^4 + (-12x^3) + 35x^3 + (-21x^2)
\][/tex]

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

So, the final expanded expression is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]

After checking the options, the correct option is:
- B. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]

This is the result of multiplying the given expressions.

Thanks for taking the time to read Multiply tex left 4x 2 7x right left 5x 2 3x right tex A tex 20x 4 35x 3 21x 2 tex B tex 20x. 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!

Rewritten by : Barada