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Which expression is equal to [tex]$(3x-5)(2x-7)$[/tex]?

A. [tex]5x^2-21x+12[/tex]
B. [tex]6x^2-31x+35[/tex]
C. [tex]6x^2-31x-12[/tex]
D. [tex]6x^2+31x-35[/tex]

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].

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