Answer :
Sure! Let's solve the problem step by step to find which expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex].
1. Expand the expression [tex]\((3x - 5)(2x - 7)\)[/tex]:
To expand this expression, we will use the distributive property (also known as the FOIL method:
- Multiply the first terms: [tex]\(3x \cdot 2x = 6x^2\)[/tex]
- Multiply the outer terms: [tex]\(3x \cdot -7 = -21x\)[/tex]
- Multiply the inner terms: [tex]\(-5 \cdot 2x = -10x\)[/tex]
- Multiply the last terms: [tex]\(-5 \cdot -7 = 35\)[/tex]
2. Combine all these products:
[tex]\[
6x^2 + (-21x) + (-10x) + 35
\][/tex]
3. Simplify by combining like terms:
[tex]\[
6x^2 - 21x - 10x + 35 = 6x^2 - 31x + 35
\][/tex]
4. Compare the expanded expression with the given choices:
The expression we found is [tex]\(6x^2 - 31x + 35\)[/tex]. Now, let's check the given options:
- [tex]\(6x^2 - 31x - 12\)[/tex]
- [tex]\(6x^2 + 31x - 35\)[/tex]
- [tex]\(5x^2 - 21x + 12\)[/tex]
- [tex]\(6x^2 - 31x + 35\)[/tex]
Based on our expansion, the correct matching expression is [tex]\(6x^2 - 31x + 35\)[/tex].
Therefore, the correct answer is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
1. Expand the expression [tex]\((3x - 5)(2x - 7)\)[/tex]:
To expand this expression, we will use the distributive property (also known as the FOIL method:
- Multiply the first terms: [tex]\(3x \cdot 2x = 6x^2\)[/tex]
- Multiply the outer terms: [tex]\(3x \cdot -7 = -21x\)[/tex]
- Multiply the inner terms: [tex]\(-5 \cdot 2x = -10x\)[/tex]
- Multiply the last terms: [tex]\(-5 \cdot -7 = 35\)[/tex]
2. Combine all these products:
[tex]\[
6x^2 + (-21x) + (-10x) + 35
\][/tex]
3. Simplify by combining like terms:
[tex]\[
6x^2 - 21x - 10x + 35 = 6x^2 - 31x + 35
\][/tex]
4. Compare the expanded expression with the given choices:
The expression we found is [tex]\(6x^2 - 31x + 35\)[/tex]. Now, let's check the given options:
- [tex]\(6x^2 - 31x - 12\)[/tex]
- [tex]\(6x^2 + 31x - 35\)[/tex]
- [tex]\(5x^2 - 21x + 12\)[/tex]
- [tex]\(6x^2 - 31x + 35\)[/tex]
Based on our expansion, the correct matching expression is [tex]\(6x^2 - 31x + 35\)[/tex].
Therefore, the correct answer is:
[tex]\[
6x^2 - 31x + 35
\][/tex]
