Answer :
To simplify [tex]\((4x - 3)(3x^2 - 4x - 3)\)[/tex], we need to apply the distributive property, which involves multiplying each term in the first polynomial by each term in the second polynomial. Let's do this step by step.
Step 1: Multiply [tex]\(4x\)[/tex] by each term in [tex]\(3x^2 - 4x - 3\)[/tex]:
1. [tex]\(4x \times 3x^2 = 12x^3\)[/tex]
2. [tex]\(4x \times -4x = -16x^2\)[/tex]
3. [tex]\(4x \times -3 = -12x\)[/tex]
Step 2: Multiply [tex]\(-3\)[/tex] by each term in [tex]\(3x^2 - 4x - 3\)[/tex]:
1. [tex]\(-3 \times 3x^2 = -9x^2\)[/tex]
2. [tex]\(-3 \times -4x = 12x\)[/tex]
3. [tex]\(-3 \times -3 = 9\)[/tex]
Step 3: Combine all the terms from the two lists:
- [tex]\(12x^3\)[/tex]
- [tex]\(-16x^2\)[/tex]
- [tex]\(-12x\)[/tex]
- [tex]\(-9x^2\)[/tex]
- [tex]\(12x\)[/tex]
- [tex]\(9\)[/tex]
Step 4: Combine like terms:
1. Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-16x^2 - 9x^2 = -25x^2\)[/tex]
2. Combine the [tex]\(x\)[/tex] terms: [tex]\(-12x + 12x = 0\)[/tex] (these terms cancel each other out)
3. The other terms remain as they are.
Final simplification:
The expression simplifies to [tex]\(12x^3 - 25x^2 + 9\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{12x^3 - 25x^2 + 9} \][/tex]
Step 1: Multiply [tex]\(4x\)[/tex] by each term in [tex]\(3x^2 - 4x - 3\)[/tex]:
1. [tex]\(4x \times 3x^2 = 12x^3\)[/tex]
2. [tex]\(4x \times -4x = -16x^2\)[/tex]
3. [tex]\(4x \times -3 = -12x\)[/tex]
Step 2: Multiply [tex]\(-3\)[/tex] by each term in [tex]\(3x^2 - 4x - 3\)[/tex]:
1. [tex]\(-3 \times 3x^2 = -9x^2\)[/tex]
2. [tex]\(-3 \times -4x = 12x\)[/tex]
3. [tex]\(-3 \times -3 = 9\)[/tex]
Step 3: Combine all the terms from the two lists:
- [tex]\(12x^3\)[/tex]
- [tex]\(-16x^2\)[/tex]
- [tex]\(-12x\)[/tex]
- [tex]\(-9x^2\)[/tex]
- [tex]\(12x\)[/tex]
- [tex]\(9\)[/tex]
Step 4: Combine like terms:
1. Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-16x^2 - 9x^2 = -25x^2\)[/tex]
2. Combine the [tex]\(x\)[/tex] terms: [tex]\(-12x + 12x = 0\)[/tex] (these terms cancel each other out)
3. The other terms remain as they are.
Final simplification:
The expression simplifies to [tex]\(12x^3 - 25x^2 + 9\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{12x^3 - 25x^2 + 9} \][/tex]
