Answer :
To determine which expression is equal to [tex]\((3x-5)(2x-7)\)[/tex], let's expand the expression step-by-step.
We will use the distributive property, also known as the FOIL method (First, Outer, Inner, Last), to expand the expression:
1. First: Multiply the first terms in each binomial:
[tex]\(3x \times 2x = 6x^2\)[/tex].
2. Outer: Multiply the outer terms in the binomials:
[tex]\(3x \times -7 = -21x\)[/tex].
3. Inner: Multiply the inner terms in the binomials:
[tex]\(-5 \times 2x = -10x\)[/tex].
4. Last: Multiply the last terms in each binomial:
[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]\[-21x - 10x = -31x\][/tex]
So, the expanded expression is:
[tex]\[6x^2 - 31x + 35\][/tex]
Let's match this with the given options:
- [tex]\(6x^2 + 31x - 35\)[/tex]
- [tex]\(6x^2 - 31x - 12\)[/tex]
- [tex]\(5x^2 - 21x + 12\)[/tex]
- [tex]\(6x^2 - 31x + 35\)[/tex]
The correct expression that matches is [tex]\(6x^2 - 31x + 35\)[/tex], so the correct choice is the fourth option.
Therefore, [tex]\((3x-5)(2x-7)\)[/tex] is equal to [tex]\(6x^2 - 31x + 35\)[/tex].
We will use the distributive property, also known as the FOIL method (First, Outer, Inner, Last), to expand the expression:
1. First: Multiply the first terms in each binomial:
[tex]\(3x \times 2x = 6x^2\)[/tex].
2. Outer: Multiply the outer terms in the binomials:
[tex]\(3x \times -7 = -21x\)[/tex].
3. Inner: Multiply the inner terms in the binomials:
[tex]\(-5 \times 2x = -10x\)[/tex].
4. Last: Multiply the last terms in each binomial:
[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]\[-21x - 10x = -31x\][/tex]
So, the expanded expression is:
[tex]\[6x^2 - 31x + 35\][/tex]
Let's match this with the given options:
- [tex]\(6x^2 + 31x - 35\)[/tex]
- [tex]\(6x^2 - 31x - 12\)[/tex]
- [tex]\(5x^2 - 21x + 12\)[/tex]
- [tex]\(6x^2 - 31x + 35\)[/tex]
The correct expression that matches is [tex]\(6x^2 - 31x + 35\)[/tex], so the correct choice is the fourth option.
Therefore, [tex]\((3x-5)(2x-7)\)[/tex] is equal to [tex]\(6x^2 - 31x + 35\)[/tex].
