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Answer :
Sure! Let's find the product of the expressions [tex]\((5x - 3)\)[/tex] and [tex]\((x^2 - 5x + 2)\)[/tex] step-by-step.
To do this, we'll use the distributive property, which involves multiplying each term in the first expression by each term in the second expression.
1. Multiply [tex]\(5x\)[/tex] by each term in the second expression:
- [tex]\(5x \times x^2 = 5x^3\)[/tex]
- [tex]\(5x \times (-5x) = -25x^2\)[/tex]
- [tex]\(5x \times 2 = 10x\)[/tex]
2. Multiply [tex]\(-3\)[/tex] by each term in the second expression:
- [tex]\(-3 \times x^2 = -3x^2\)[/tex]
- [tex]\(-3 \times (-5x) = 15x\)[/tex]
- [tex]\(-3 \times 2 = -6\)[/tex]
3. Combine all the results:
- [tex]\(5x^3\)[/tex]
- [tex]\(-25x^2 + (-3x^2) = -28x^2\)[/tex]
- [tex]\(10x + 15x = 25x\)[/tex]
- [tex]\(-6\)[/tex]
4. Write down the final expanded expression:
[tex]\[
5x^3 - 28x^2 + 25x - 6
\][/tex]
So, the product of the expressions [tex]\((5x-3)\)[/tex] and [tex]\((x^2-5x+2)\)[/tex] is [tex]\(5x^3 - 28x^2 + 25x - 6\)[/tex].
This matches option G: [tex]\(5x^3 - 28x^2 + 25x - 6\)[/tex].
To do this, we'll use the distributive property, which involves multiplying each term in the first expression by each term in the second expression.
1. Multiply [tex]\(5x\)[/tex] by each term in the second expression:
- [tex]\(5x \times x^2 = 5x^3\)[/tex]
- [tex]\(5x \times (-5x) = -25x^2\)[/tex]
- [tex]\(5x \times 2 = 10x\)[/tex]
2. Multiply [tex]\(-3\)[/tex] by each term in the second expression:
- [tex]\(-3 \times x^2 = -3x^2\)[/tex]
- [tex]\(-3 \times (-5x) = 15x\)[/tex]
- [tex]\(-3 \times 2 = -6\)[/tex]
3. Combine all the results:
- [tex]\(5x^3\)[/tex]
- [tex]\(-25x^2 + (-3x^2) = -28x^2\)[/tex]
- [tex]\(10x + 15x = 25x\)[/tex]
- [tex]\(-6\)[/tex]
4. Write down the final expanded expression:
[tex]\[
5x^3 - 28x^2 + 25x - 6
\][/tex]
So, the product of the expressions [tex]\((5x-3)\)[/tex] and [tex]\((x^2-5x+2)\)[/tex] is [tex]\(5x^3 - 28x^2 + 25x - 6\)[/tex].
This matches option G: [tex]\(5x^3 - 28x^2 + 25x - 6\)[/tex].
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