Answer :
Sure! Let's go through the process of multiplying the given polynomials step-by-step:
We have the polynomials [tex]\( (4x^2 + 4x + 6) \)[/tex] and [tex]\( (7x + 5) \)[/tex].
To multiply these polynomials, we'll use the distributive property (also known as the FOIL method when dealing with two binomials), which means we'll multiply each term in the first polynomial by each term in the second polynomial. Here's how it works:
1. Multiply the first term of the first polynomial by each term in the second polynomial:
- [tex]\(4x^2 \cdot 7x = 28x^3\)[/tex]
- [tex]\(4x^2 \cdot 5 = 20x^2\)[/tex]
2. Multiply the second term of the first polynomial by each term in the second polynomial:
- [tex]\(4x \cdot 7x = 28x^2\)[/tex]
- [tex]\(4x \cdot 5 = 20x\)[/tex]
3. Multiply the third term of the first polynomial by each term in the second polynomial:
- [tex]\(6 \cdot 7x = 42x\)[/tex]
- [tex]\(6 \cdot 5 = 30\)[/tex]
Now, we combine all these results:
[tex]\[
28x^3 + 20x^2 + 28x^2 + 20x + 42x + 30
\][/tex]
Next, we'll combine like terms:
- For [tex]\(x^3\)[/tex]: [tex]\(28x^3\)[/tex]
- For [tex]\(x^2\)[/tex]: [tex]\(20x^2 + 28x^2 = 48x^2\)[/tex]
- For [tex]\(x\)[/tex]: [tex]\(20x + 42x = 62x\)[/tex]
- The constant term: [tex]\(30\)[/tex]
So, the final result of multiplying the polynomials is:
[tex]\[
28x^3 + 48x^2 + 62x + 30
\][/tex]
The answer that matches this expression is option B: [tex]\(28x^3 + 48x^2 + 62x + 30\)[/tex].
We have the polynomials [tex]\( (4x^2 + 4x + 6) \)[/tex] and [tex]\( (7x + 5) \)[/tex].
To multiply these polynomials, we'll use the distributive property (also known as the FOIL method when dealing with two binomials), which means we'll multiply each term in the first polynomial by each term in the second polynomial. Here's how it works:
1. Multiply the first term of the first polynomial by each term in the second polynomial:
- [tex]\(4x^2 \cdot 7x = 28x^3\)[/tex]
- [tex]\(4x^2 \cdot 5 = 20x^2\)[/tex]
2. Multiply the second term of the first polynomial by each term in the second polynomial:
- [tex]\(4x \cdot 7x = 28x^2\)[/tex]
- [tex]\(4x \cdot 5 = 20x\)[/tex]
3. Multiply the third term of the first polynomial by each term in the second polynomial:
- [tex]\(6 \cdot 7x = 42x\)[/tex]
- [tex]\(6 \cdot 5 = 30\)[/tex]
Now, we combine all these results:
[tex]\[
28x^3 + 20x^2 + 28x^2 + 20x + 42x + 30
\][/tex]
Next, we'll combine like terms:
- For [tex]\(x^3\)[/tex]: [tex]\(28x^3\)[/tex]
- For [tex]\(x^2\)[/tex]: [tex]\(20x^2 + 28x^2 = 48x^2\)[/tex]
- For [tex]\(x\)[/tex]: [tex]\(20x + 42x = 62x\)[/tex]
- The constant term: [tex]\(30\)[/tex]
So, the final result of multiplying the polynomials is:
[tex]\[
28x^3 + 48x^2 + 62x + 30
\][/tex]
The answer that matches this expression is option B: [tex]\(28x^3 + 48x^2 + 62x + 30\)[/tex].
