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Answer :
We start with the expression
[tex]$$
(4x - 3)(3x^2 - 4x - 3).
$$[/tex]
First, we use the distributive property to expand the product. Multiply each term in the first parenthesis by each term in the second:
1. Multiply [tex]\(4x\)[/tex] by each term in [tex]\(3x^2 - 4x - 3\)[/tex]:
[tex]\[
4x \cdot 3x^2 = 12x^3,
\][/tex]
[tex]\[
4x \cdot (-4x) = -16x^2,
\][/tex]
[tex]\[
4x \cdot (-3) = -12x.
\][/tex]
2. Multiply [tex]\(-3\)[/tex] by each term in [tex]\(3x^2 - 4x - 3\)[/tex]:
[tex]\[
-3 \cdot 3x^2 = -9x^2,
\][/tex]
[tex]\[
-3 \cdot (-4x) = 12x,
\][/tex]
[tex]\[
-3 \cdot (-3) = 9.
\][/tex]
Now, we write all these terms together:
[tex]$$
12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9.
$$[/tex]
Next, combine like terms:
- The [tex]\(x^3\)[/tex] term: [tex]\(12x^3\)[/tex].
- The [tex]\(x^2\)[/tex] terms: [tex]\(-16x^2 - 9x^2 = -25x^2\)[/tex].
- The [tex]\(x\)[/tex] terms: [tex]\(-12x + 12x = 0\)[/tex].
- The constant: [tex]\(9\)[/tex].
Thus, the simplified expression is:
[tex]$$
12x^3 - 25x^2 + 9.
$$[/tex]
Comparing with the options provided:
1. [tex]\(12x^3 + 25x^2 + 9\)[/tex]
2. [tex]\(12x^3 - 25x^2 - 9\)[/tex]
3. [tex]\(12x^3 + 25x^2 - 9\)[/tex]
4. [tex]\(12x^3 - 25x^2 + 9\)[/tex]
The correct answer is option 4.
[tex]$$
(4x - 3)(3x^2 - 4x - 3).
$$[/tex]
First, we use the distributive property to expand the product. Multiply each term in the first parenthesis by each term in the second:
1. Multiply [tex]\(4x\)[/tex] by each term in [tex]\(3x^2 - 4x - 3\)[/tex]:
[tex]\[
4x \cdot 3x^2 = 12x^3,
\][/tex]
[tex]\[
4x \cdot (-4x) = -16x^2,
\][/tex]
[tex]\[
4x \cdot (-3) = -12x.
\][/tex]
2. Multiply [tex]\(-3\)[/tex] by each term in [tex]\(3x^2 - 4x - 3\)[/tex]:
[tex]\[
-3 \cdot 3x^2 = -9x^2,
\][/tex]
[tex]\[
-3 \cdot (-4x) = 12x,
\][/tex]
[tex]\[
-3 \cdot (-3) = 9.
\][/tex]
Now, we write all these terms together:
[tex]$$
12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9.
$$[/tex]
Next, combine like terms:
- The [tex]\(x^3\)[/tex] term: [tex]\(12x^3\)[/tex].
- The [tex]\(x^2\)[/tex] terms: [tex]\(-16x^2 - 9x^2 = -25x^2\)[/tex].
- The [tex]\(x\)[/tex] terms: [tex]\(-12x + 12x = 0\)[/tex].
- The constant: [tex]\(9\)[/tex].
Thus, the simplified expression is:
[tex]$$
12x^3 - 25x^2 + 9.
$$[/tex]
Comparing with the options provided:
1. [tex]\(12x^3 + 25x^2 + 9\)[/tex]
2. [tex]\(12x^3 - 25x^2 - 9\)[/tex]
3. [tex]\(12x^3 + 25x^2 - 9\)[/tex]
4. [tex]\(12x^3 - 25x^2 + 9\)[/tex]
The correct answer is option 4.
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