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Answer :
To multiply the polynomials [tex]\((4x^2 + 4x + 6)\)[/tex] and [tex]\((7x + 5)\)[/tex], follow these steps:
1. Distribute each term in the first polynomial to every term in the second polynomial:
- 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]
- 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]
- 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. Add all the resulting terms together:
[tex]\[
28x^3 + 20x^2 + 28x^2 + 20x + 42x + 30
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(20x^2 + 28x^2 = 48x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(20x + 42x = 62x\)[/tex]
4. Write the final expanded expression:
[tex]\[
28x^3 + 48x^2 + 62x + 30
\][/tex]
Thus, the correct answer is [tex]\(\boxed{28x^3 + 48x^2 + 62x + 30}\)[/tex], which matches option A.
1. Distribute each term in the first polynomial to every term in the second polynomial:
- 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]
- 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]
- 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. Add all the resulting terms together:
[tex]\[
28x^3 + 20x^2 + 28x^2 + 20x + 42x + 30
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(20x^2 + 28x^2 = 48x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(20x + 42x = 62x\)[/tex]
4. Write the final expanded expression:
[tex]\[
28x^3 + 48x^2 + 62x + 30
\][/tex]
Thus, the correct answer is [tex]\(\boxed{28x^3 + 48x^2 + 62x + 30}\)[/tex], which matches option A.
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