Answer :
Sure, let's multiply the polynomials [tex]\((4x^2 + 4x + 6)(7x + 5)\)[/tex] step by step.
1. Distribute each term in the first polynomial with each term in the second polynomial:
- Multiply [tex]\(4x^2\)[/tex] by each term in [tex]\(7x + 5\)[/tex]:
- [tex]\(4x^2 \cdot 7x = 28x^3\)[/tex]
- [tex]\(4x^2 \cdot 5 = 20x^2\)[/tex]
- Multiply [tex]\(4x\)[/tex] by each term in [tex]\(7x + 5\)[/tex]:
- [tex]\(4x \cdot 7x = 28x^2\)[/tex]
- [tex]\(4x \cdot 5 = 20x\)[/tex]
- Multiply [tex]\(6\)[/tex] by each term in [tex]\(7x + 5\)[/tex]:
- [tex]\(6 \cdot 7x = 42x\)[/tex]
- [tex]\(6 \cdot 5 = 30\)[/tex]
2. Combine all the products:
[tex]\[
28x^3 + 20x^2 + 28x^2 + 20x + 42x + 30
\][/tex]
3. Combine like terms:
- Combine [tex]\(x^2\)[/tex] terms:
[tex]\[20x^2 + 28x^2 = 48x^2\][/tex]
- Combine [tex]\(x\)[/tex] terms:
[tex]\[20x + 42x = 62x\][/tex]
4. Write the final expression:
[tex]\[
28x^3 + 48x^2 + 62x + 30
\][/tex]
The expanded polynomial is [tex]\(28x^3 + 48x^2 + 62x + 30\)[/tex], which corresponds to option A.
1. Distribute each term in the first polynomial with each term in the second polynomial:
- Multiply [tex]\(4x^2\)[/tex] by each term in [tex]\(7x + 5\)[/tex]:
- [tex]\(4x^2 \cdot 7x = 28x^3\)[/tex]
- [tex]\(4x^2 \cdot 5 = 20x^2\)[/tex]
- Multiply [tex]\(4x\)[/tex] by each term in [tex]\(7x + 5\)[/tex]:
- [tex]\(4x \cdot 7x = 28x^2\)[/tex]
- [tex]\(4x \cdot 5 = 20x\)[/tex]
- Multiply [tex]\(6\)[/tex] by each term in [tex]\(7x + 5\)[/tex]:
- [tex]\(6 \cdot 7x = 42x\)[/tex]
- [tex]\(6 \cdot 5 = 30\)[/tex]
2. Combine all the products:
[tex]\[
28x^3 + 20x^2 + 28x^2 + 20x + 42x + 30
\][/tex]
3. Combine like terms:
- Combine [tex]\(x^2\)[/tex] terms:
[tex]\[20x^2 + 28x^2 = 48x^2\][/tex]
- Combine [tex]\(x\)[/tex] terms:
[tex]\[20x + 42x = 62x\][/tex]
4. Write the final expression:
[tex]\[
28x^3 + 48x^2 + 62x + 30
\][/tex]
The expanded polynomial is [tex]\(28x^3 + 48x^2 + 62x + 30\)[/tex], which corresponds to option A.
