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Answer :
Sure! Let's multiply the polynomials step-by-step:
We're given the polynomials [tex]\((4x^2 + 4x + 6)\)[/tex] and [tex]\((7x + 5)\)[/tex]. We'll distribute each term in the first polynomial to every term in the second polynomial.
1. Distribute [tex]\(4x^2\)[/tex]:
- [tex]\(4x^2 \times 7x = 28x^3\)[/tex]
- [tex]\(4x^2 \times 5 = 20x^2\)[/tex]
After this step, we have: [tex]\(28x^3 + 20x^2\)[/tex].
2. Distribute [tex]\(4x\)[/tex]:
- [tex]\(4x \times 7x = 28x^2\)[/tex]
- [tex]\(4x \times 5 = 20x\)[/tex]
Adding these terms to the previous result:
[tex]\[28x^3 + 20x^2 + 28x^2 + 20x\][/tex]
3. Distribute [tex]\(6\)[/tex]:
- [tex]\(6 \times 7x = 42x\)[/tex]
- [tex]\(6 \times 5 = 30\)[/tex]
Adding these terms as well:
[tex]\[28x^3 + 20x^2 + 28x^2 + 20x + 42x + 30\][/tex]
4. 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]
Finally, our expression is:
[tex]\[28x^3 + 48x^2 + 62x + 30\][/tex]
So the correct answer is [tex]\(\boxed{28x^3 + 48x^2 + 62x + 30}\)[/tex], which matches option B.
We're given the polynomials [tex]\((4x^2 + 4x + 6)\)[/tex] and [tex]\((7x + 5)\)[/tex]. We'll distribute each term in the first polynomial to every term in the second polynomial.
1. Distribute [tex]\(4x^2\)[/tex]:
- [tex]\(4x^2 \times 7x = 28x^3\)[/tex]
- [tex]\(4x^2 \times 5 = 20x^2\)[/tex]
After this step, we have: [tex]\(28x^3 + 20x^2\)[/tex].
2. Distribute [tex]\(4x\)[/tex]:
- [tex]\(4x \times 7x = 28x^2\)[/tex]
- [tex]\(4x \times 5 = 20x\)[/tex]
Adding these terms to the previous result:
[tex]\[28x^3 + 20x^2 + 28x^2 + 20x\][/tex]
3. Distribute [tex]\(6\)[/tex]:
- [tex]\(6 \times 7x = 42x\)[/tex]
- [tex]\(6 \times 5 = 30\)[/tex]
Adding these terms as well:
[tex]\[28x^3 + 20x^2 + 28x^2 + 20x + 42x + 30\][/tex]
4. 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]
Finally, our expression is:
[tex]\[28x^3 + 48x^2 + 62x + 30\][/tex]
So the correct answer is [tex]\(\boxed{28x^3 + 48x^2 + 62x + 30}\)[/tex], which matches option B.
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