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Answer :
Sure! Let's simplify the expression [tex]\((4x - 3)(3x^2 - 4x - 3)\)[/tex] step by step.
1. Distribution: We will distribute each term in the first parenthesis by each term in the second parenthesis.
- Start with [tex]\(4x\)[/tex]:
- [tex]\(4x \times 3x^2 = 12x^3\)[/tex]
- [tex]\(4x \times -4x = -16x^2\)[/tex]
- [tex]\(4x \times -3 = -12x\)[/tex]
- Now distribute [tex]\(-3\)[/tex]:
- [tex]\(-3 \times 3x^2 = -9x^2\)[/tex]
- [tex]\(-3 \times -4x = 12x\)[/tex]
- [tex]\(-3 \times -3 = 9\)[/tex]
2. Combine like terms: Now we add up all the terms we have.
- Cubic term ([tex]\(x^3\)[/tex]):
- We only have one [tex]\(x^3\)[/tex] term: [tex]\(12x^3\)[/tex]
- Quadratic terms ([tex]\(x^2\)[/tex]):
- Combine [tex]\(-16x^2\)[/tex] and [tex]\(-9x^2\)[/tex]:
- [tex]\(-16x^2 - 9x^2 = -25x^2\)[/tex]
- Linear terms ([tex]\(x\)[/tex]):
- Combine [tex]\(-12x\)[/tex] and [tex]\(12x\)[/tex]:
- [tex]\(-12x + 12x = 0\)[/tex] (these cancel out)
- Constant term:
- We have one constant: [tex]\(9\)[/tex]
3. Final simplified expression: Putting it all together, the simplified expression is:
[tex]\[
12x^3 - 25x^2 + 0x + 9
\][/tex]
Since the linear term is zero, it simplifies to:
[tex]\[
12x^3 - 25x^2 + 9
\][/tex]
So, the correct simplification is [tex]\(12x^3 - 25x^2 + 9\)[/tex]. Therefore, the correct option is [tex]\(12x^3 - 25x^2 + 9\)[/tex].
1. Distribution: We will distribute each term in the first parenthesis by each term in the second parenthesis.
- Start with [tex]\(4x\)[/tex]:
- [tex]\(4x \times 3x^2 = 12x^3\)[/tex]
- [tex]\(4x \times -4x = -16x^2\)[/tex]
- [tex]\(4x \times -3 = -12x\)[/tex]
- Now distribute [tex]\(-3\)[/tex]:
- [tex]\(-3 \times 3x^2 = -9x^2\)[/tex]
- [tex]\(-3 \times -4x = 12x\)[/tex]
- [tex]\(-3 \times -3 = 9\)[/tex]
2. Combine like terms: Now we add up all the terms we have.
- Cubic term ([tex]\(x^3\)[/tex]):
- We only have one [tex]\(x^3\)[/tex] term: [tex]\(12x^3\)[/tex]
- Quadratic terms ([tex]\(x^2\)[/tex]):
- Combine [tex]\(-16x^2\)[/tex] and [tex]\(-9x^2\)[/tex]:
- [tex]\(-16x^2 - 9x^2 = -25x^2\)[/tex]
- Linear terms ([tex]\(x\)[/tex]):
- Combine [tex]\(-12x\)[/tex] and [tex]\(12x\)[/tex]:
- [tex]\(-12x + 12x = 0\)[/tex] (these cancel out)
- Constant term:
- We have one constant: [tex]\(9\)[/tex]
3. Final simplified expression: Putting it all together, the simplified expression is:
[tex]\[
12x^3 - 25x^2 + 0x + 9
\][/tex]
Since the linear term is zero, it simplifies to:
[tex]\[
12x^3 - 25x^2 + 9
\][/tex]
So, the correct simplification is [tex]\(12x^3 - 25x^2 + 9\)[/tex]. Therefore, the correct option is [tex]\(12x^3 - 25x^2 + 9\)[/tex].
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