Answer :
To simplify the expression [tex]\((6x - 5)(2x^2 - 3x - 6)\)[/tex], we need to use the distributive property, which involves multiplying each term in the first parenthesis by each term in the second parenthesis. Here's a step-by-step breakdown of the multiplication:
1. Distribute [tex]\(6x\)[/tex] across the trinomial [tex]\((2x^2 - 3x - 6)\)[/tex]:
- [tex]\(6x \cdot 2x^2 = 12x^3\)[/tex]
- [tex]\(6x \cdot (-3x) = -18x^2\)[/tex]
- [tex]\(6x \cdot (-6) = -36x\)[/tex]
2. Distribute [tex]\(-5\)[/tex] across the trinomial [tex]\((2x^2 - 3x - 6)\)[/tex]:
- [tex]\(-5 \cdot 2x^2 = -10x^2\)[/tex]
- [tex]\(-5 \cdot (-3x) = 15x\)[/tex]
- [tex]\(-5 \cdot (-6) = 30\)[/tex]
3. Combine all the terms obtained from the multiplication:
- [tex]\(12x^3\)[/tex]
- [tex]\(-18x^2 - 10x^2 = -28x^2\)[/tex] (Combine the [tex]\(x^2\)[/tex] terms)
- [tex]\(-36x + 15x = -21x\)[/tex] (Combine the [tex]\(x\)[/tex] terms)
- [tex]\(+ 30\)[/tex]
4. Write the simplified expression:
The simplified expression is [tex]\(12x^3 - 28x^2 - 21x + 30\)[/tex].
Therefore, the correct simplification of the expression is [tex]\(\boxed{12x^3 - 28x^2 - 21x + 30}\)[/tex], which matches the option given in the problem choices.
1. Distribute [tex]\(6x\)[/tex] across the trinomial [tex]\((2x^2 - 3x - 6)\)[/tex]:
- [tex]\(6x \cdot 2x^2 = 12x^3\)[/tex]
- [tex]\(6x \cdot (-3x) = -18x^2\)[/tex]
- [tex]\(6x \cdot (-6) = -36x\)[/tex]
2. Distribute [tex]\(-5\)[/tex] across the trinomial [tex]\((2x^2 - 3x - 6)\)[/tex]:
- [tex]\(-5 \cdot 2x^2 = -10x^2\)[/tex]
- [tex]\(-5 \cdot (-3x) = 15x\)[/tex]
- [tex]\(-5 \cdot (-6) = 30\)[/tex]
3. Combine all the terms obtained from the multiplication:
- [tex]\(12x^3\)[/tex]
- [tex]\(-18x^2 - 10x^2 = -28x^2\)[/tex] (Combine the [tex]\(x^2\)[/tex] terms)
- [tex]\(-36x + 15x = -21x\)[/tex] (Combine the [tex]\(x\)[/tex] terms)
- [tex]\(+ 30\)[/tex]
4. Write the simplified expression:
The simplified expression is [tex]\(12x^3 - 28x^2 - 21x + 30\)[/tex].
Therefore, the correct simplification of the expression is [tex]\(\boxed{12x^3 - 28x^2 - 21x + 30}\)[/tex], which matches the option given in the problem choices.
