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Answer :
To find which expression is equal to [tex]\((3x-5)(2x-7)\)[/tex], we need to expand the expression by using the distributive property (also known as the FOIL method for binomials, which stands for First, Outer, Inner, Last).
Here's the step-by-step expansion:
1. First: Multiply the first terms of each binomial:
[tex]\(3x \times 2x = 6x^2\)[/tex].
2. Outer: Multiply the outer terms:
[tex]\(3x \times (-7) = -21x\)[/tex].
3. Inner: Multiply the inner terms:
[tex]\(-5 \times 2x = -10x\)[/tex].
4. Last: Multiply the last terms:
[tex]\(-5 \times (-7) = 35\)[/tex].
Now, combine all these results:
[tex]\[6x^2 - 21x - 10x + 35\][/tex]
Combine the like terms ([tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]):
[tex]\[6x^2 - 31x + 35\][/tex]
This means the expanded form of [tex]\((3x-5)(2x-7)\)[/tex] is [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].
Here's the step-by-step expansion:
1. First: Multiply the first terms of each binomial:
[tex]\(3x \times 2x = 6x^2\)[/tex].
2. Outer: Multiply the outer terms:
[tex]\(3x \times (-7) = -21x\)[/tex].
3. Inner: Multiply the inner terms:
[tex]\(-5 \times 2x = -10x\)[/tex].
4. Last: Multiply the last terms:
[tex]\(-5 \times (-7) = 35\)[/tex].
Now, combine all these results:
[tex]\[6x^2 - 21x - 10x + 35\][/tex]
Combine the like terms ([tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]):
[tex]\[6x^2 - 31x + 35\][/tex]
This means the expanded form of [tex]\((3x-5)(2x-7)\)[/tex] is [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].
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