We appreciate your visit to Multiply the polynomials tex left 7x 2 5x 7 right 4x 6 tex A tex 28x 3 22x 2 2x 42 tex B tex 28x. 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]\((7x^2 + 5x + 7)\)[/tex] and [tex]\((4x - 6)\)[/tex], we need to use the distributive property, which involves multiplying each term in the first polynomial by each term in the second polynomial. Here are the steps:
1. Multiply the first term of [tex]\(7x^2 + 5x + 7\)[/tex] by each term in [tex]\(4x - 6\)[/tex]:
- [tex]\( 7x^2 \times 4x = 28x^3 \)[/tex]
- [tex]\( 7x^2 \times -6 = -42x^2 \)[/tex]
2. Multiply the second term of [tex]\(7x^2 + 5x + 7\)[/tex] by each term in [tex]\(4x - 6\)[/tex]:
- [tex]\( 5x \times 4x = 20x^2 \)[/tex]
- [tex]\( 5x \times -6 = -30x \)[/tex]
3. Multiply the third term of [tex]\(7x^2 + 5x + 7\)[/tex] by each term in [tex]\(4x - 6\)[/tex]:
- [tex]\( 7 \times 4x = 28x \)[/tex]
- [tex]\( 7 \times -6 = -42 \)[/tex]
4. Combine all these results:
- Collect all the terms: [tex]\(28x^3, -42x^2, 20x^2, -30x, 28x, -42\)[/tex].
5. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-42x^2 + 20x^2 = -22x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-30x + 28x = -2x\)[/tex]
6. Write the final expression:
- The multiplied polynomial is [tex]\[ 28x^3 - 22x^2 - 2x - 42 \][/tex]
Therefore, the correct answer is C. [tex]\(28x^3 - 22x^2 - 2x - 42\)[/tex].
1. Multiply the first term of [tex]\(7x^2 + 5x + 7\)[/tex] by each term in [tex]\(4x - 6\)[/tex]:
- [tex]\( 7x^2 \times 4x = 28x^3 \)[/tex]
- [tex]\( 7x^2 \times -6 = -42x^2 \)[/tex]
2. Multiply the second term of [tex]\(7x^2 + 5x + 7\)[/tex] by each term in [tex]\(4x - 6\)[/tex]:
- [tex]\( 5x \times 4x = 20x^2 \)[/tex]
- [tex]\( 5x \times -6 = -30x \)[/tex]
3. Multiply the third term of [tex]\(7x^2 + 5x + 7\)[/tex] by each term in [tex]\(4x - 6\)[/tex]:
- [tex]\( 7 \times 4x = 28x \)[/tex]
- [tex]\( 7 \times -6 = -42 \)[/tex]
4. Combine all these results:
- Collect all the terms: [tex]\(28x^3, -42x^2, 20x^2, -30x, 28x, -42\)[/tex].
5. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-42x^2 + 20x^2 = -22x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-30x + 28x = -2x\)[/tex]
6. Write the final expression:
- The multiplied polynomial is [tex]\[ 28x^3 - 22x^2 - 2x - 42 \][/tex]
Therefore, the correct answer is C. [tex]\(28x^3 - 22x^2 - 2x - 42\)[/tex].
Thanks for taking the time to read Multiply the polynomials tex left 7x 2 5x 7 right 4x 6 tex A tex 28x 3 22x 2 2x 42 tex B tex 28x. 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
