We appreciate your visit to Multiply the polynomials tex 7x 2 5x 7 4x 6 tex A tex 28x 3 62x 2 2x 42 tex B tex 28x 3 22x. 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!
Answer :
To multiply the polynomials [tex]\((7x^2 + 5x + 7)(4x - 6)\)[/tex], we use the distributive property, also known as the FOIL method for binomials, to ensure each term in the first polynomial is multiplied by each term in the second polynomial.
1. Multiply each term of the first polynomial by each term of the second polynomial:
- Multiply [tex]\(7x^2\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
7x^2 \cdot 4x = 28x^3
\][/tex]
- Multiply [tex]\(7x^2\)[/tex] by [tex]\(-6\)[/tex]:
[tex]\[
7x^2 \cdot (-6) = -42x^2
\][/tex]
- Multiply [tex]\(5x\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
5x \cdot 4x = 20x^2
\][/tex]
- Multiply [tex]\(5x\)[/tex] by [tex]\(-6\)[/tex]:
[tex]\[
5x \cdot (-6) = -30x
\][/tex]
- Multiply [tex]\(7\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
7 \cdot 4x = 28x
\][/tex]
- Multiply [tex]\(7\)[/tex] by [tex]\(-6\)[/tex]:
[tex]\[
7 \cdot (-6) = -42
\][/tex]
2. Combine all these terms:
- Start with the cubic term:
[tex]\[
28x^3
\][/tex]
- Combine the quadratic terms [tex]\( -42x^2 \)[/tex] and [tex]\( 20x^2 \)[/tex]:
[tex]\[
-42x^2 + 20x^2 = -22x^2
\][/tex]
- Combine the linear terms [tex]\( -30x \)[/tex] and [tex]\( 28x \)[/tex]:
[tex]\[
-30x + 28x = -2x
\][/tex]
- Finally, add the constant term:
[tex]\[
-42
\][/tex]
3. Write the final expression:
The product of the polynomials is:
[tex]\[
28x^3 - 22x^2 - 2x - 42
\][/tex]
The correct choice is D: [tex]\(28x^3 - 22x^2 - 2x - 42\)[/tex].
1. Multiply each term of the first polynomial by each term of the second polynomial:
- Multiply [tex]\(7x^2\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
7x^2 \cdot 4x = 28x^3
\][/tex]
- Multiply [tex]\(7x^2\)[/tex] by [tex]\(-6\)[/tex]:
[tex]\[
7x^2 \cdot (-6) = -42x^2
\][/tex]
- Multiply [tex]\(5x\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
5x \cdot 4x = 20x^2
\][/tex]
- Multiply [tex]\(5x\)[/tex] by [tex]\(-6\)[/tex]:
[tex]\[
5x \cdot (-6) = -30x
\][/tex]
- Multiply [tex]\(7\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
7 \cdot 4x = 28x
\][/tex]
- Multiply [tex]\(7\)[/tex] by [tex]\(-6\)[/tex]:
[tex]\[
7 \cdot (-6) = -42
\][/tex]
2. Combine all these terms:
- Start with the cubic term:
[tex]\[
28x^3
\][/tex]
- Combine the quadratic terms [tex]\( -42x^2 \)[/tex] and [tex]\( 20x^2 \)[/tex]:
[tex]\[
-42x^2 + 20x^2 = -22x^2
\][/tex]
- Combine the linear terms [tex]\( -30x \)[/tex] and [tex]\( 28x \)[/tex]:
[tex]\[
-30x + 28x = -2x
\][/tex]
- Finally, add the constant term:
[tex]\[
-42
\][/tex]
3. Write the final expression:
The product of the polynomials is:
[tex]\[
28x^3 - 22x^2 - 2x - 42
\][/tex]
The correct choice is D: [tex]\(28x^3 - 22x^2 - 2x - 42\)[/tex].
Thanks for taking the time to read Multiply the polynomials tex 7x 2 5x 7 4x 6 tex A tex 28x 3 62x 2 2x 42 tex B tex 28x 3 22x. 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!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
