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Answer :
Sure! Let's multiply the polynomials step by step.
We are given two polynomials:
- [tex]\(4x^2 + 4x + 6\)[/tex]
- [tex]\(7x + 5\)[/tex]
To find the product of these two polynomials, we need to multiply each term in the first polynomial by each term in the second polynomial and then combine like terms.
Step 1: Distribute each term in [tex]\((4x^2 + 4x + 6)\)[/tex] with each term in [tex]\((7x + 5)\)[/tex].
1. Multiply [tex]\(4x^2\)[/tex] by each term:
- [tex]\(4x^2 \times 7x = 28x^3\)[/tex]
- [tex]\(4x^2 \times 5 = 20x^2\)[/tex]
2. Multiply [tex]\(4x\)[/tex] by each term:
- [tex]\(4x \times 7x = 28x^2\)[/tex]
- [tex]\(4x \times 5 = 20x\)[/tex]
3. Multiply [tex]\(6\)[/tex] by each term:
- [tex]\(6 \times 7x = 42x\)[/tex]
- [tex]\(6 \times 5 = 30\)[/tex]
Step 2: Combine the like terms.
- Combine the [tex]\(x^3\)[/tex] terms:
- [tex]\(28x^3\)[/tex]
- 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]
- The constant term:
- [tex]\(30\)[/tex]
Step 3: Write the final result.
The polynomial after combining like terms is:
[tex]\[28x^3 + 48x^2 + 62x + 30\][/tex]
So, the correct answer is:
A. [tex]\(28x^3 + 48x^2 + 62x + 30\)[/tex]
We are given two polynomials:
- [tex]\(4x^2 + 4x + 6\)[/tex]
- [tex]\(7x + 5\)[/tex]
To find the product of these two polynomials, we need to multiply each term in the first polynomial by each term in the second polynomial and then combine like terms.
Step 1: Distribute each term in [tex]\((4x^2 + 4x + 6)\)[/tex] with each term in [tex]\((7x + 5)\)[/tex].
1. Multiply [tex]\(4x^2\)[/tex] by each term:
- [tex]\(4x^2 \times 7x = 28x^3\)[/tex]
- [tex]\(4x^2 \times 5 = 20x^2\)[/tex]
2. Multiply [tex]\(4x\)[/tex] by each term:
- [tex]\(4x \times 7x = 28x^2\)[/tex]
- [tex]\(4x \times 5 = 20x\)[/tex]
3. Multiply [tex]\(6\)[/tex] by each term:
- [tex]\(6 \times 7x = 42x\)[/tex]
- [tex]\(6 \times 5 = 30\)[/tex]
Step 2: Combine the like terms.
- Combine the [tex]\(x^3\)[/tex] terms:
- [tex]\(28x^3\)[/tex]
- 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]
- The constant term:
- [tex]\(30\)[/tex]
Step 3: Write the final result.
The polynomial after combining like terms is:
[tex]\[28x^3 + 48x^2 + 62x + 30\][/tex]
So, the correct answer is:
A. [tex]\(28x^3 + 48x^2 + 62x + 30\)[/tex]
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