Answer :
We begin by expanding the product
[tex]$$
(6x-5)(2x^2-3x-6)
$$[/tex]
using the distributive property.
1. Multiply each term in the first factor by each term in the second factor:
- Multiply [tex]\(6x\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]$$
6x \cdot 2x^2 = 12x^3.
$$[/tex]
- Multiply [tex]\(6x\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]$$
6x \cdot (-3x) = -18x^2.
$$[/tex]
- Multiply [tex]\(6x\)[/tex] by [tex]\(-6\)[/tex]:
[tex]$$
6x \cdot (-6) = -36x.
$$[/tex]
- Multiply [tex]\(-5\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]$$
-5 \cdot 2x^2 = -10x^2.
$$[/tex]
- Multiply [tex]\(-5\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]$$
-5 \cdot (-3x) = 15x.
$$[/tex]
- Multiply [tex]\(-5\)[/tex] by [tex]\(-6\)[/tex]:
[tex]$$
-5 \cdot (-6) = 30.
$$[/tex]
2. Now, combine like terms:
- The [tex]\(x^3\)[/tex]-term:
[tex]$$
12x^3.
$$[/tex]
- Combine the [tex]\(x^2\)[/tex]-terms:
[tex]$$
-18x^2 - 10x^2 = -28x^2.
$$[/tex]
- Combine the [tex]\(x\)[/tex]-terms:
[tex]$$
-36x + 15x = -21x.
$$[/tex]
- The constant term remains:
[tex]$$
30.
$$[/tex]
So, the simplified expression is
[tex]$$
12x^3-28x^2-21x+30.
$$[/tex]
Therefore, the correct simplification is
[tex]$$
12x^3-28x^2-21x+30.
$$[/tex]
[tex]$$
(6x-5)(2x^2-3x-6)
$$[/tex]
using the distributive property.
1. Multiply each term in the first factor by each term in the second factor:
- Multiply [tex]\(6x\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]$$
6x \cdot 2x^2 = 12x^3.
$$[/tex]
- Multiply [tex]\(6x\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]$$
6x \cdot (-3x) = -18x^2.
$$[/tex]
- Multiply [tex]\(6x\)[/tex] by [tex]\(-6\)[/tex]:
[tex]$$
6x \cdot (-6) = -36x.
$$[/tex]
- Multiply [tex]\(-5\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]$$
-5 \cdot 2x^2 = -10x^2.
$$[/tex]
- Multiply [tex]\(-5\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]$$
-5 \cdot (-3x) = 15x.
$$[/tex]
- Multiply [tex]\(-5\)[/tex] by [tex]\(-6\)[/tex]:
[tex]$$
-5 \cdot (-6) = 30.
$$[/tex]
2. Now, combine like terms:
- The [tex]\(x^3\)[/tex]-term:
[tex]$$
12x^3.
$$[/tex]
- Combine the [tex]\(x^2\)[/tex]-terms:
[tex]$$
-18x^2 - 10x^2 = -28x^2.
$$[/tex]
- Combine the [tex]\(x\)[/tex]-terms:
[tex]$$
-36x + 15x = -21x.
$$[/tex]
- The constant term remains:
[tex]$$
30.
$$[/tex]
So, the simplified expression is
[tex]$$
12x^3-28x^2-21x+30.
$$[/tex]
Therefore, the correct simplification is
[tex]$$
12x^3-28x^2-21x+30.
$$[/tex]
