Answer :
To simplify the expression [tex]\((4x - 3)(3x^2 - 4x - 3)\)[/tex], let's go through the multiplication step by step.
1. Multiply each term in the first binomial by each term in the second binomial.
Distribute [tex]\(4x\)[/tex] to each term in the second binomial:
[tex]\[
4x \cdot 3x^2 = 12x^3
\][/tex]
[tex]\[
4x \cdot (-4x) = -16x^2
\][/tex]
[tex]\[
4x \cdot (-3) = -12x
\][/tex]
Distribute [tex]\(-3\)[/tex] to each term in the second binomial:
[tex]\[
(-3) \cdot 3x^2 = -9x^2
\][/tex]
[tex]\[
(-3) \cdot (-4x) = 12x
\][/tex]
[tex]\[
(-3) \cdot (-3) = 9
\][/tex]
2. Combine all these products:
[tex]\[
12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9
\][/tex]
3. Simplify by combining like terms:
Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
-16x^2 - 9x^2 = -25x^2
\][/tex]
Combine the [tex]\(x\)[/tex] terms:
[tex]\[
-12x + 12x = 0
\][/tex]
So, the expression simplifies to:
[tex]\[
12x^3 - 25x^2 + 9
\][/tex]
Therefore, the correct simplified expression is:
[tex]\[
12x^3 - 25x^2 + 9
\][/tex]
This corresponds to option d).
1. Multiply each term in the first binomial by each term in the second binomial.
Distribute [tex]\(4x\)[/tex] to each term in the second binomial:
[tex]\[
4x \cdot 3x^2 = 12x^3
\][/tex]
[tex]\[
4x \cdot (-4x) = -16x^2
\][/tex]
[tex]\[
4x \cdot (-3) = -12x
\][/tex]
Distribute [tex]\(-3\)[/tex] to each term in the second binomial:
[tex]\[
(-3) \cdot 3x^2 = -9x^2
\][/tex]
[tex]\[
(-3) \cdot (-4x) = 12x
\][/tex]
[tex]\[
(-3) \cdot (-3) = 9
\][/tex]
2. Combine all these products:
[tex]\[
12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9
\][/tex]
3. Simplify by combining like terms:
Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
-16x^2 - 9x^2 = -25x^2
\][/tex]
Combine the [tex]\(x\)[/tex] terms:
[tex]\[
-12x + 12x = 0
\][/tex]
So, the expression simplifies to:
[tex]\[
12x^3 - 25x^2 + 9
\][/tex]
Therefore, the correct simplified expression is:
[tex]\[
12x^3 - 25x^2 + 9
\][/tex]
This corresponds to option d).
