Answer :
To simplify the expression [tex]\((6x - 5)(2x^2 - 3x - 6)\)[/tex], we can use the distributive property and multiply each term in the first polynomial by each term in the second polynomial. Here’s how you can do it step-by-step:
1. Distribute [tex]\(6x\)[/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]:
- [tex]\(-5 \cdot 2x^2 = -10x^2\)[/tex]
- [tex]\(-5 \cdot (-3x) = 15x\)[/tex]
- [tex]\(-5 \cdot (-6) = 30\)[/tex]
3. Combine all terms:
- Combine [tex]\(x^3\)[/tex] terms: [tex]\(12x^3\)[/tex]
- Combine [tex]\(x^2\)[/tex] terms: [tex]\(-18x^2 - 10x^2 = -28x^2\)[/tex]
- Combine [tex]\(x\)[/tex] terms: [tex]\(-36x + 15x = -21x\)[/tex]
- Combine constant terms: [tex]\(30\)[/tex]
After combining all the terms, the simplified expression is:
[tex]\[ 12x^3 - 28x^2 - 21x + 30 \][/tex]
So, the correct simplification is: [tex]\(12x^3 - 28x^2 - 21x + 30\)[/tex].
1. Distribute [tex]\(6x\)[/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]:
- [tex]\(-5 \cdot 2x^2 = -10x^2\)[/tex]
- [tex]\(-5 \cdot (-3x) = 15x\)[/tex]
- [tex]\(-5 \cdot (-6) = 30\)[/tex]
3. Combine all terms:
- Combine [tex]\(x^3\)[/tex] terms: [tex]\(12x^3\)[/tex]
- Combine [tex]\(x^2\)[/tex] terms: [tex]\(-18x^2 - 10x^2 = -28x^2\)[/tex]
- Combine [tex]\(x\)[/tex] terms: [tex]\(-36x + 15x = -21x\)[/tex]
- Combine constant terms: [tex]\(30\)[/tex]
After combining all the terms, the simplified expression is:
[tex]\[ 12x^3 - 28x^2 - 21x + 30 \][/tex]
So, the correct simplification is: [tex]\(12x^3 - 28x^2 - 21x + 30\)[/tex].
