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Answer :
To multiply the polynomials [tex]\((4x^2 + 4x + 6)\)[/tex] and [tex]\((7x + 5)\)[/tex], we can use the distributive property. This property allows us to multiply each term in the first polynomial by each term in the second polynomial and then combine like terms.
Let's break it down step by step:
1. Multiply each term in [tex]\(4x^2 + 4x + 6\)[/tex] by each term in [tex]\(7x + 5\)[/tex]:
- First, multiply [tex]\(4x^2\)[/tex] by each term in [tex]\(7x + 5\)[/tex]:
- [tex]\(4x^2 \times 7x = 28x^3\)[/tex]
- [tex]\(4x^2 \times 5 = 20x^2\)[/tex]
- Next, multiply [tex]\(4x\)[/tex] by each term in [tex]\(7x + 5\)[/tex]:
- [tex]\(4x \times 7x = 28x^2\)[/tex]
- [tex]\(4x \times 5 = 20x\)[/tex]
- Finally, multiply [tex]\(6\)[/tex] by each term in [tex]\(7x + 5\)[/tex]:
- [tex]\(6 \times 7x = 42x\)[/tex]
- [tex]\(6 \times 5 = 30\)[/tex]
2. Combine all the terms:
- From the above calculations:
- We have one [tex]\(x^3\)[/tex] term: [tex]\(28x^3\)[/tex]
- We have two [tex]\(x^2\)[/tex] terms: [tex]\(20x^2\)[/tex] and [tex]\(28x^2\)[/tex], which combine to [tex]\(48x^2\)[/tex]
- We have two [tex]\(x\)[/tex] terms: [tex]\(20x\)[/tex] and [tex]\(42x\)[/tex], which combine to [tex]\(62x\)[/tex]
- We have one constant term: [tex]\(30\)[/tex]
3. Write the final expression:
[tex]\[
28x^3 + 48x^2 + 62x + 30
\][/tex]
Based on the calculations, the correct answer is:
C. [tex]\(28x^3 + 48x^2 + 62x + 30\)[/tex]
Let's break it down step by step:
1. Multiply each term in [tex]\(4x^2 + 4x + 6\)[/tex] by each term in [tex]\(7x + 5\)[/tex]:
- First, multiply [tex]\(4x^2\)[/tex] by each term in [tex]\(7x + 5\)[/tex]:
- [tex]\(4x^2 \times 7x = 28x^3\)[/tex]
- [tex]\(4x^2 \times 5 = 20x^2\)[/tex]
- Next, multiply [tex]\(4x\)[/tex] by each term in [tex]\(7x + 5\)[/tex]:
- [tex]\(4x \times 7x = 28x^2\)[/tex]
- [tex]\(4x \times 5 = 20x\)[/tex]
- Finally, multiply [tex]\(6\)[/tex] by each term in [tex]\(7x + 5\)[/tex]:
- [tex]\(6 \times 7x = 42x\)[/tex]
- [tex]\(6 \times 5 = 30\)[/tex]
2. Combine all the terms:
- From the above calculations:
- We have one [tex]\(x^3\)[/tex] term: [tex]\(28x^3\)[/tex]
- We have two [tex]\(x^2\)[/tex] terms: [tex]\(20x^2\)[/tex] and [tex]\(28x^2\)[/tex], which combine to [tex]\(48x^2\)[/tex]
- We have two [tex]\(x\)[/tex] terms: [tex]\(20x\)[/tex] and [tex]\(42x\)[/tex], which combine to [tex]\(62x\)[/tex]
- We have one constant term: [tex]\(30\)[/tex]
3. Write the final expression:
[tex]\[
28x^3 + 48x^2 + 62x + 30
\][/tex]
Based on the calculations, the correct answer is:
C. [tex]\(28x^3 + 48x^2 + 62x + 30\)[/tex]
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