Answer :
To determine which expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex], we need to expand and simplify the expression.
Step 1: Expand the expression
We'll use the distributive property (also known as the FOIL method for binomials) to expand [tex]\((3x - 5)(2x - 7)\)[/tex].
1. First Terms: Multiply the first terms in each binomial:
[tex]\[ 3x \times 2x = 6x^2 \][/tex]
2. Outer Terms: Multiply the outer terms:
[tex]\[ 3x \times -7 = -21x \][/tex]
3. Inner Terms: Multiply the inner terms:
[tex]\[ -5 \times 2x = -10x \][/tex]
4. Last Terms: Multiply the last terms:
[tex]\[ -5 \times -7 = 35 \][/tex]
Step 2: Combine like terms
Combine the results from the expansion:
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-21x - 10x = -31x\)[/tex].
Now, put it all together:
[tex]\[ 6x^2 - 31x + 35 \][/tex]
Conclusion:
The expression [tex]\((3x - 5)(2x - 7)\)[/tex] simplifies to [tex]\(6x^2 - 31x + 35\)[/tex].
Therefore, the expression that is equal to [tex]\((3x - 5)(2x - 7)\)[/tex] is [tex]\(6x^2 - 31x + 35\)[/tex].
So, the correct choice is [tex]\(\boxed{6x^2 - 31x + 35}\)[/tex].
Step 1: Expand the expression
We'll use the distributive property (also known as the FOIL method for binomials) to expand [tex]\((3x - 5)(2x - 7)\)[/tex].
1. First Terms: Multiply the first terms in each binomial:
[tex]\[ 3x \times 2x = 6x^2 \][/tex]
2. Outer Terms: Multiply the outer terms:
[tex]\[ 3x \times -7 = -21x \][/tex]
3. Inner Terms: Multiply the inner terms:
[tex]\[ -5 \times 2x = -10x \][/tex]
4. Last Terms: Multiply the last terms:
[tex]\[ -5 \times -7 = 35 \][/tex]
Step 2: Combine like terms
Combine the results from the expansion:
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-21x - 10x = -31x\)[/tex].
Now, put it all together:
[tex]\[ 6x^2 - 31x + 35 \][/tex]
Conclusion:
The expression [tex]\((3x - 5)(2x - 7)\)[/tex] simplifies to [tex]\(6x^2 - 31x + 35\)[/tex].
Therefore, the expression that is equal to [tex]\((3x - 5)(2x - 7)\)[/tex] is [tex]\(6x^2 - 31x + 35\)[/tex].
So, the correct choice is [tex]\(\boxed{6x^2 - 31x + 35}\)[/tex].
