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Answer :
To multiply the polynomials
[tex]$$
(4x^2 + 4x + 6)(7x + 5),
$$[/tex]
we distribute each term in the first polynomial to each term in the second polynomial.
1. Multiply each term in the first polynomial by the first term in the second polynomial:
[tex]\[
4x^2 \cdot 7x = 28x^3,
\][/tex]
[tex]\[
4x \cdot 7x = 28x^2,
\][/tex]
[tex]\[
6 \cdot 7x = 42x.
\][/tex]
2. Multiply each term in the first polynomial by the second term in the second polynomial:
[tex]\[
4x^2 \cdot 5 = 20x^2,
\][/tex]
[tex]\[
4x \cdot 5 = 20x,
\][/tex]
[tex]\[
6 \cdot 5 = 30.
\][/tex]
3. Combine like terms:
- The only [tex]$x^3$[/tex] term is:
[tex]\[
28x^3.
\][/tex]
- Combine the [tex]$x^2$[/tex] terms:
[tex]\[
28x^2 + 20x^2 = 48x^2.
\][/tex]
- Combine the [tex]$x$[/tex] terms:
[tex]\[
42x + 20x = 62x.
\][/tex]
- The constant term is:
[tex]\[
30.
\][/tex]
Thus, the expanded product is:
[tex]$$
28x^3 + 48x^2 + 62x + 30.
$$[/tex]
Therefore, the correct answer is option A:
[tex]$$
28x^3 + 48x^2 + 62x + 30.
$$[/tex]
[tex]$$
(4x^2 + 4x + 6)(7x + 5),
$$[/tex]
we distribute each term in the first polynomial to each term in the second polynomial.
1. Multiply each term in the first polynomial by the first term in the second polynomial:
[tex]\[
4x^2 \cdot 7x = 28x^3,
\][/tex]
[tex]\[
4x \cdot 7x = 28x^2,
\][/tex]
[tex]\[
6 \cdot 7x = 42x.
\][/tex]
2. Multiply each term in the first polynomial by the second term in the second polynomial:
[tex]\[
4x^2 \cdot 5 = 20x^2,
\][/tex]
[tex]\[
4x \cdot 5 = 20x,
\][/tex]
[tex]\[
6 \cdot 5 = 30.
\][/tex]
3. Combine like terms:
- The only [tex]$x^3$[/tex] term is:
[tex]\[
28x^3.
\][/tex]
- Combine the [tex]$x^2$[/tex] terms:
[tex]\[
28x^2 + 20x^2 = 48x^2.
\][/tex]
- Combine the [tex]$x$[/tex] terms:
[tex]\[
42x + 20x = 62x.
\][/tex]
- The constant term is:
[tex]\[
30.
\][/tex]
Thus, the expanded product is:
[tex]$$
28x^3 + 48x^2 + 62x + 30.
$$[/tex]
Therefore, the correct answer is option A:
[tex]$$
28x^3 + 48x^2 + 62x + 30.
$$[/tex]
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