Answer :
Sure! Let's multiply the polynomials step-by-step.
The given polynomials are [tex]\((4x^2 + 3x + 7)\)[/tex] and [tex]\((8x - 5)\)[/tex].
To multiply these polynomials, we need to distribute each term in the first polynomial with each term in the second polynomial.
First, we distribute [tex]\(4x^2\)[/tex] to both terms in [tex]\(8x - 5\)[/tex]:
[tex]\[ 4x^2 \cdot 8x = 32x^3 \][/tex]
[tex]\[ 4x^2 \cdot (-5) = -20x^2 \][/tex]
Next, we distribute [tex]\(3x\)[/tex] to both terms in [tex]\(8x - 5\)[/tex]:
[tex]\[ 3x \cdot 8x = 24x^2 \][/tex]
[tex]\[ 3x \cdot (-5) = -15x \][/tex]
Finally, we distribute [tex]\(7\)[/tex] to both terms in [tex]\(8x - 5\)[/tex]:
[tex]\[ 7 \cdot 8x = 56x \][/tex]
[tex]\[ 7 \cdot (-5) = -35 \][/tex]
Now, let's combine all these results:
[tex]\[ 32x^3 - 20x^2 + 24x^2 - 15x + 56x - 35 \][/tex]
We combine like terms ([tex]\(x^2\)[/tex] terms, and [tex]\(x\)[/tex] terms):
[tex]\[ 32x^3 + ( -20x^2 + 24x^2 ) + ( -15x + 56x ) - 35 \][/tex]
This simplifies to:
[tex]\[ 32x^3 + 4x^2 + 41x - 35 \][/tex]
So, the correct answer is:
[tex]\[ \boxed{32x^3 + 4x^2 + 41x - 35} \][/tex]
Therefore, the correct answer is:
[tex]\[ \text{A. } 32x^3 + 4x^2 + 41x - 35 \][/tex]
The given polynomials are [tex]\((4x^2 + 3x + 7)\)[/tex] and [tex]\((8x - 5)\)[/tex].
To multiply these polynomials, we need to distribute each term in the first polynomial with each term in the second polynomial.
First, we distribute [tex]\(4x^2\)[/tex] to both terms in [tex]\(8x - 5\)[/tex]:
[tex]\[ 4x^2 \cdot 8x = 32x^3 \][/tex]
[tex]\[ 4x^2 \cdot (-5) = -20x^2 \][/tex]
Next, we distribute [tex]\(3x\)[/tex] to both terms in [tex]\(8x - 5\)[/tex]:
[tex]\[ 3x \cdot 8x = 24x^2 \][/tex]
[tex]\[ 3x \cdot (-5) = -15x \][/tex]
Finally, we distribute [tex]\(7\)[/tex] to both terms in [tex]\(8x - 5\)[/tex]:
[tex]\[ 7 \cdot 8x = 56x \][/tex]
[tex]\[ 7 \cdot (-5) = -35 \][/tex]
Now, let's combine all these results:
[tex]\[ 32x^3 - 20x^2 + 24x^2 - 15x + 56x - 35 \][/tex]
We combine like terms ([tex]\(x^2\)[/tex] terms, and [tex]\(x\)[/tex] terms):
[tex]\[ 32x^3 + ( -20x^2 + 24x^2 ) + ( -15x + 56x ) - 35 \][/tex]
This simplifies to:
[tex]\[ 32x^3 + 4x^2 + 41x - 35 \][/tex]
So, the correct answer is:
[tex]\[ \boxed{32x^3 + 4x^2 + 41x - 35} \][/tex]
Therefore, the correct answer is:
[tex]\[ \text{A. } 32x^3 + 4x^2 + 41x - 35 \][/tex]
