Answer :
To find the expression that is equal to [tex]\((x-3)(2x^2-x+3)\)[/tex], we need to expand and simplify it. Let’s break it down step-by-step:
1. Distribute [tex]\( (x-3) \)[/tex] with each term in [tex]\( (2x^2-x+3) \)[/tex]:
- Distribute [tex]\( x \)[/tex] across [tex]\( 2x^2 - x + 3 \)[/tex]:
- [tex]\( x \times 2x^2 = 2x^3 \)[/tex]
- [tex]\( x \times (-x) = -x^2 \)[/tex]
- [tex]\( x \times 3 = 3x \)[/tex]
- Distribute [tex]\(-3\)[/tex] across [tex]\( 2x^2 - x + 3 \)[/tex]:
- [tex]\(-3 \times 2x^2 = -6x^2 \)[/tex]
- [tex]\(-3 \times (-x) = 3x \)[/tex]
- [tex]\(-3 \times 3 = -9 \)[/tex]
2. Combine all the results:
[tex]\[
2x^3 + (-x^2) + 3x - 6x^2 + 3x - 9
\][/tex]
3. Simplify by combining like terms:
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\(-x^2 - 6x^2 = -7x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms:
[tex]\(3x + 3x = 6x\)[/tex]
- Combine all simplified terms to form the final polynomial expression:
[tex]\[
2x^3 - 7x^2 + 6x - 9
\][/tex]
Therefore, the expression that is equal to [tex]\((x-3)(2x^2-x+3)\)[/tex] is [tex]\(2x^3 - 7x^2 + 6x - 9\)[/tex]. This corresponds to the first option in the given choices.
1. Distribute [tex]\( (x-3) \)[/tex] with each term in [tex]\( (2x^2-x+3) \)[/tex]:
- Distribute [tex]\( x \)[/tex] across [tex]\( 2x^2 - x + 3 \)[/tex]:
- [tex]\( x \times 2x^2 = 2x^3 \)[/tex]
- [tex]\( x \times (-x) = -x^2 \)[/tex]
- [tex]\( x \times 3 = 3x \)[/tex]
- Distribute [tex]\(-3\)[/tex] across [tex]\( 2x^2 - x + 3 \)[/tex]:
- [tex]\(-3 \times 2x^2 = -6x^2 \)[/tex]
- [tex]\(-3 \times (-x) = 3x \)[/tex]
- [tex]\(-3 \times 3 = -9 \)[/tex]
2. Combine all the results:
[tex]\[
2x^3 + (-x^2) + 3x - 6x^2 + 3x - 9
\][/tex]
3. Simplify by combining like terms:
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\(-x^2 - 6x^2 = -7x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms:
[tex]\(3x + 3x = 6x\)[/tex]
- Combine all simplified terms to form the final polynomial expression:
[tex]\[
2x^3 - 7x^2 + 6x - 9
\][/tex]
Therefore, the expression that is equal to [tex]\((x-3)(2x^2-x+3)\)[/tex] is [tex]\(2x^3 - 7x^2 + 6x - 9\)[/tex]. This corresponds to the first option in the given choices.
