Answer :
Let's multiply the polynomials [tex]\((4x^2 + 4x + 6)\)[/tex] and [tex]\((7x + 5)\)[/tex] step-by-step.
1. Distribute each term in the first polynomial by each term in the second polynomial:
- First, distribute [tex]\(4x^2\)[/tex] across [tex]\((7x + 5)\)[/tex]:
[tex]\[
4x^2 \cdot 7x = 28x^3
\][/tex]
[tex]\[
4x^2 \cdot 5 = 20x^2
\][/tex]
- Next, distribute [tex]\(4x\)[/tex] across [tex]\((7x + 5)\)[/tex]:
[tex]\[
4x \cdot 7x = 28x^2
\][/tex]
[tex]\[
4x \cdot 5 = 20x
\][/tex]
- Finally, distribute [tex]\(6\)[/tex] across [tex]\((7x + 5)\)[/tex]:
[tex]\[
6 \cdot 7x = 42x
\][/tex]
[tex]\[
6 \cdot 5 = 30
\][/tex]
2. Add up all the terms:
- Combine the results:
[tex]\[
28x^3 + 20x^2 + 28x^2 + 20x + 42x + 30
\][/tex]
3. Combine like terms:
- Group and add the like terms together:
- The [tex]\(x^3\)[/tex] term: [tex]\(28x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(20x^2 + 28x^2 = 48x^2\)[/tex]
- The [tex]\(x\)[/tex] terms: [tex]\(20x + 42x = 62x\)[/tex]
- The constant term: [tex]\(30\)[/tex]
4. Write the simplified expression:
[tex]\[
28x^3 + 48x^2 + 62x + 30
\][/tex]
The correct answer is B. [tex]\(28x^3 + 48x^2 + 62x + 30\)[/tex].
1. Distribute each term in the first polynomial by each term in the second polynomial:
- First, distribute [tex]\(4x^2\)[/tex] across [tex]\((7x + 5)\)[/tex]:
[tex]\[
4x^2 \cdot 7x = 28x^3
\][/tex]
[tex]\[
4x^2 \cdot 5 = 20x^2
\][/tex]
- Next, distribute [tex]\(4x\)[/tex] across [tex]\((7x + 5)\)[/tex]:
[tex]\[
4x \cdot 7x = 28x^2
\][/tex]
[tex]\[
4x \cdot 5 = 20x
\][/tex]
- Finally, distribute [tex]\(6\)[/tex] across [tex]\((7x + 5)\)[/tex]:
[tex]\[
6 \cdot 7x = 42x
\][/tex]
[tex]\[
6 \cdot 5 = 30
\][/tex]
2. Add up all the terms:
- Combine the results:
[tex]\[
28x^3 + 20x^2 + 28x^2 + 20x + 42x + 30
\][/tex]
3. Combine like terms:
- Group and add the like terms together:
- The [tex]\(x^3\)[/tex] term: [tex]\(28x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(20x^2 + 28x^2 = 48x^2\)[/tex]
- The [tex]\(x\)[/tex] terms: [tex]\(20x + 42x = 62x\)[/tex]
- The constant term: [tex]\(30\)[/tex]
4. Write the simplified expression:
[tex]\[
28x^3 + 48x^2 + 62x + 30
\][/tex]
The correct answer is B. [tex]\(28x^3 + 48x^2 + 62x + 30\)[/tex].
