Answer :
Let's solve the problem by multiplying the given polynomials step-by-step.
We need to multiply [tex]\((4x^2 + 4x + 6)(7x + 5)\)[/tex].
### Step 1: Distribute each term in the first polynomial to each term in the second polynomial.
1. 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]
2. 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]
3. Multiply [tex]\(6\)[/tex] by each term in [tex]\( (7x + 5) \)[/tex]:
- [tex]\(6 \times 7x = 42x\)[/tex]
- [tex]\(6 \times 5 = 30\)[/tex]
### Step 2: Write down all the products.
- From the distribution, we have:
- [tex]\(28x^3\)[/tex]
- [tex]\(20x^2 + 28x^2 = 48x^2\)[/tex] (Combine like terms)
- [tex]\(20x + 42x = 62x\)[/tex] (Combine like terms)
- [tex]\(30\)[/tex]
### Final Result
Putting it all together, the resulting polynomial is:
[tex]\[28x^3 + 48x^2 + 62x + 30\][/tex]
So, the correct answer is:
[tex]\[ \text{D. } 28x^3 + 48x^2 + 62x + 30 \][/tex]
We need to multiply [tex]\((4x^2 + 4x + 6)(7x + 5)\)[/tex].
### Step 1: Distribute each term in the first polynomial to each term in the second polynomial.
1. 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]
2. 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]
3. Multiply [tex]\(6\)[/tex] by each term in [tex]\( (7x + 5) \)[/tex]:
- [tex]\(6 \times 7x = 42x\)[/tex]
- [tex]\(6 \times 5 = 30\)[/tex]
### Step 2: Write down all the products.
- From the distribution, we have:
- [tex]\(28x^3\)[/tex]
- [tex]\(20x^2 + 28x^2 = 48x^2\)[/tex] (Combine like terms)
- [tex]\(20x + 42x = 62x\)[/tex] (Combine like terms)
- [tex]\(30\)[/tex]
### Final Result
Putting it all together, the resulting polynomial is:
[tex]\[28x^3 + 48x^2 + 62x + 30\][/tex]
So, the correct answer is:
[tex]\[ \text{D. } 28x^3 + 48x^2 + 62x + 30 \][/tex]
