Answer :
Sure! Let's go through the steps of multiplying the polynomials:
[tex]\[
(7x^2 + 5x + 7)(4x - 6)
\][/tex]
We'll multiply each term in the first polynomial by each term in the second polynomial and then combine like terms.
1. Multiply [tex]\(7x^2\)[/tex] by [tex]\(4x\)[/tex] and [tex]\(-6\)[/tex]:
[tex]\[
7x^2 \cdot 4x = 28x^3
\][/tex]
[tex]\[
7x^2 \cdot (-6) = -42x^2
\][/tex]
2. Multiply [tex]\(5x\)[/tex] by [tex]\(4x\)[/tex] and [tex]\(-6\)[/tex]:
[tex]\[
5x \cdot 4x = 20x^2
\][/tex]
[tex]\[
5x \cdot (-6) = -30x
\][/tex]
3. Multiply [tex]\(7\)[/tex] by [tex]\(4x\)[/tex] and [tex]\(-6\)[/tex]:
[tex]\[
7 \cdot 4x = 28x
\][/tex]
[tex]\[
7 \cdot (-6) = -42
\][/tex]
Now, let's combine all these terms:
[tex]\[
28x^3 + (-42x^2 + 20x^2) + (-30x + 28x) - 42
\][/tex]
Simplify by combining like terms:
1. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
-42x^2 + 20x^2 = -22x^2
\][/tex]
2. Combine the [tex]\(x\)[/tex] terms:
[tex]\[
-30x + 28x = -2x
\][/tex]
So, the resulting polynomial is:
[tex]\[
28x^3 - 22x^2 - 2x - 42
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{A. \ 28x^3 - 22x^2 - 2x - 42}
\][/tex]
[tex]\[
(7x^2 + 5x + 7)(4x - 6)
\][/tex]
We'll multiply each term in the first polynomial by each term in the second polynomial and then combine like terms.
1. Multiply [tex]\(7x^2\)[/tex] by [tex]\(4x\)[/tex] and [tex]\(-6\)[/tex]:
[tex]\[
7x^2 \cdot 4x = 28x^3
\][/tex]
[tex]\[
7x^2 \cdot (-6) = -42x^2
\][/tex]
2. Multiply [tex]\(5x\)[/tex] by [tex]\(4x\)[/tex] and [tex]\(-6\)[/tex]:
[tex]\[
5x \cdot 4x = 20x^2
\][/tex]
[tex]\[
5x \cdot (-6) = -30x
\][/tex]
3. Multiply [tex]\(7\)[/tex] by [tex]\(4x\)[/tex] and [tex]\(-6\)[/tex]:
[tex]\[
7 \cdot 4x = 28x
\][/tex]
[tex]\[
7 \cdot (-6) = -42
\][/tex]
Now, let's combine all these terms:
[tex]\[
28x^3 + (-42x^2 + 20x^2) + (-30x + 28x) - 42
\][/tex]
Simplify by combining like terms:
1. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
-42x^2 + 20x^2 = -22x^2
\][/tex]
2. Combine the [tex]\(x\)[/tex] terms:
[tex]\[
-30x + 28x = -2x
\][/tex]
So, the resulting polynomial is:
[tex]\[
28x^3 - 22x^2 - 2x - 42
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{A. \ 28x^3 - 22x^2 - 2x - 42}
\][/tex]
