Answer :
To find which expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex], we need to expand the expression using the distributive property (also known as the FOIL method for binomials). Here’s how it works step-by-step:
1. Multiply the First terms:
- [tex]\(3x \times 2x = 6x^2\)[/tex]
2. Multiply the Outer terms:
- [tex]\(3x \times -7 = -21x\)[/tex]
3. Multiply the Inner terms:
- [tex]\(-5 \times 2x = -10x\)[/tex]
4. Multiply the Last terms:
- [tex]\(-5 \times -7 = 35\)[/tex]
Now, combine all these results into a single expression:
[tex]\[6x^2 - 21x - 10x + 35\][/tex]
Next, combine the like terms ([tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]):
[tex]\[6x^2 - 31x + 35\][/tex]
This is the expanded form of the expression [tex]\((3x - 5)(2x - 7)\)[/tex].
Now, let's identify which choice matches this expression:
- [tex]\(6x^2 - 31x + 35\)[/tex] is the form we have.
This matches the fourth choice: [tex]\(6x^2 - 31x + 35\)[/tex].
1. Multiply the First terms:
- [tex]\(3x \times 2x = 6x^2\)[/tex]
2. Multiply the Outer terms:
- [tex]\(3x \times -7 = -21x\)[/tex]
3. Multiply the Inner terms:
- [tex]\(-5 \times 2x = -10x\)[/tex]
4. Multiply the Last terms:
- [tex]\(-5 \times -7 = 35\)[/tex]
Now, combine all these results into a single expression:
[tex]\[6x^2 - 21x - 10x + 35\][/tex]
Next, combine the like terms ([tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]):
[tex]\[6x^2 - 31x + 35\][/tex]
This is the expanded form of the expression [tex]\((3x - 5)(2x - 7)\)[/tex].
Now, let's identify which choice matches this expression:
- [tex]\(6x^2 - 31x + 35\)[/tex] is the form we have.
This matches the fourth choice: [tex]\(6x^2 - 31x + 35\)[/tex].
