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Answer :
To determine which expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex], let's follow these steps:
1. Distribute each term in the first binomial by each term in the second binomial:
[tex]\[(3x - 5)(2x - 7)\][/tex]
First, distribute [tex]\(3x\)[/tex] to both [tex]\(2x\)[/tex] and [tex]\(-7\)[/tex]:
[tex]\[3x \cdot 2x = 6x^2\][/tex]
[tex]\[3x \cdot (-7) = -21x\][/tex]
Next, distribute [tex]\(-5\)[/tex] to both [tex]\(2x\)[/tex] and [tex]\(-7\)[/tex]:
[tex]\[-5 \cdot 2x = -10x\][/tex]
[tex]\[-5 \cdot (-7) = 35\][/tex]
2. Combine all the products:
[tex]\[6x^2 - 21x - 10x + 35\][/tex]
3. Simplify by combining like terms:
[tex]\[-21x\][/tex] and [tex]\[-10x\][/tex] are like terms (both have [tex]\(x\)[/tex] as a factor):
[tex]\[6x^2 - 31x + 35\][/tex]
So, the expression equal to [tex]\((3x - 5)(2x - 7)\)[/tex] is:
[tex]\[6x^2 - 31x + 35\][/tex]
Thus, the correct answer is:
[tex]\[6x^2 - 31x + 35\][/tex]
1. Distribute each term in the first binomial by each term in the second binomial:
[tex]\[(3x - 5)(2x - 7)\][/tex]
First, distribute [tex]\(3x\)[/tex] to both [tex]\(2x\)[/tex] and [tex]\(-7\)[/tex]:
[tex]\[3x \cdot 2x = 6x^2\][/tex]
[tex]\[3x \cdot (-7) = -21x\][/tex]
Next, distribute [tex]\(-5\)[/tex] to both [tex]\(2x\)[/tex] and [tex]\(-7\)[/tex]:
[tex]\[-5 \cdot 2x = -10x\][/tex]
[tex]\[-5 \cdot (-7) = 35\][/tex]
2. Combine all the products:
[tex]\[6x^2 - 21x - 10x + 35\][/tex]
3. Simplify by combining like terms:
[tex]\[-21x\][/tex] and [tex]\[-10x\][/tex] are like terms (both have [tex]\(x\)[/tex] as a factor):
[tex]\[6x^2 - 31x + 35\][/tex]
So, the expression equal to [tex]\((3x - 5)(2x - 7)\)[/tex] is:
[tex]\[6x^2 - 31x + 35\][/tex]
Thus, the correct answer is:
[tex]\[6x^2 - 31x + 35\][/tex]
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