Answer :
To find which expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex], we'll expand the expression by using the distributive property, often referred to as the FOIL method (First, Outside, Inside, Last) for binomials.
Let's go through the steps:
1. First Terms: Multiply the first terms in each binomial:
[tex]\(3x \times 2x = 6x^2\)[/tex]
2. Outside Terms: Multiply the outer terms:
[tex]\(3x \times -7 = -21x\)[/tex]
3. Inside Terms: Multiply the inner terms:
[tex]\(-5 \times 2x = -10x\)[/tex]
4. Last Terms: Multiply the last terms:
[tex]\(-5 \times -7 = 35\)[/tex]
Next, combine all these results:
- The expression now is: [tex]\(6x^2 - 21x - 10x + 35\)[/tex]
Combine the like terms ([tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]):
- [tex]\(-21x - 10x = -31x\)[/tex]
Thus, the fully expanded expression is:
[tex]\[ 6x^2 - 31x + 35 \][/tex]
This matches the fourth option given: [tex]\(6x^2 - 31x + 35\)[/tex].
So, the correct expression equal to [tex]\((3x-5)(2x-7)\)[/tex] is:
[tex]\[ 6x^2 - 31x + 35 \][/tex]
Let's go through the steps:
1. First Terms: Multiply the first terms in each binomial:
[tex]\(3x \times 2x = 6x^2\)[/tex]
2. Outside Terms: Multiply the outer terms:
[tex]\(3x \times -7 = -21x\)[/tex]
3. Inside Terms: Multiply the inner terms:
[tex]\(-5 \times 2x = -10x\)[/tex]
4. Last Terms: Multiply the last terms:
[tex]\(-5 \times -7 = 35\)[/tex]
Next, combine all these results:
- The expression now is: [tex]\(6x^2 - 21x - 10x + 35\)[/tex]
Combine the like terms ([tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]):
- [tex]\(-21x - 10x = -31x\)[/tex]
Thus, the fully expanded expression is:
[tex]\[ 6x^2 - 31x + 35 \][/tex]
This matches the fourth option given: [tex]\(6x^2 - 31x + 35\)[/tex].
So, the correct expression equal to [tex]\((3x-5)(2x-7)\)[/tex] is:
[tex]\[ 6x^2 - 31x + 35 \][/tex]
