College

We appreciate your visit to Choose the correct simplification of tex 7x 2 6x 3x 2 4 tex A tex 21x 4 42x 3 28x 2 tex B tex 42x. 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!

Choose the correct simplification of [tex]7x^2(6x + 3x^2 - 4)[/tex].

A. [tex]21x^4 - 42x^3 + 28x^2[/tex]

B. [tex]42x^4 + 21x^3 - 3x^2[/tex]

C. [tex]21x^4 + 42x^3 - 28x^2[/tex]

D. [tex]42x^4 - 13x^3 + 11x^2[/tex]

Answer :

Sure! Let's simplify the expression [tex]\(7x^2(6x + 3x^2 - 4)\)[/tex] step by step.

1. Distribute [tex]\(7x^2\)[/tex] through each term inside the parentheses:

[tex]\[
7x^2 \cdot 6x + 7x^2 \cdot 3x^2 + 7x^2 \cdot (-4)
\][/tex]

2. Calculate the product for each term:

- For the first term: [tex]\(7x^2 \cdot 6x\)[/tex]
[tex]\[
7 \cdot 6 \cdot x^2 \cdot x = 42x^3
\][/tex]

- For the second term: [tex]\(7x^2 \cdot 3x^2\)[/tex]
[tex]\[
7 \cdot 3 \cdot x^2 \cdot x^2 = 21x^4
\][/tex]

- For the third term: [tex]\(7x^2 \cdot (-4)\)[/tex]
[tex]\[
7 \cdot (-4) \cdot x^2 = -28x^2
\][/tex]

3. Combine all the terms:

[tex]\[
21x^4 + 42x^3 - 28x^2
\][/tex]

So, the correct simplification of [tex]\(7x^2(6x + 3x^2 - 4)\)[/tex] is:

[tex]\(21x^4 + 42x^3 - 28x^2\)[/tex]

Among the given options:

- [tex]\(21x^4 - 42x^3 + 28x^2\)[/tex]
- [tex]\(42x^4 + 21x^3 - 3x^2\)[/tex]
- [tex]\(21x^4 + 42x^3 - 28x^2\)[/tex]
- [tex]\(42x^4 - 13x^3 + 11x^2\)[/tex]

The correct option is:

[tex]\(21x^4 + 42x^3 - 28x^2\)[/tex]

Therefore, the correct simplification is provided by the third option:

[tex]\[
\boxed{21x^4 + 42x^3 - 28x^2}
\][/tex]

Thanks for taking the time to read Choose the correct simplification of tex 7x 2 6x 3x 2 4 tex A tex 21x 4 42x 3 28x 2 tex B tex 42x. 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

Other Questions