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Answer :
To solve the problem of determining which expression is equal to [tex]\((3x - 5)(2x - 7)\)[/tex], we need to expand the product using the distributive property. Here are the steps:
1. Apply the distributive property (also known as the FOIL method for binomials):
- First terms: Multiply the first terms from each binomial:
[tex]\[ 3x \times 2x = 6x^2 \][/tex]
- Outer terms: Multiply the outer terms:
[tex]\[ 3x \times -7 = -21x \][/tex]
- Inner terms: Multiply the inner terms:
[tex]\[ -5 \times 2x = -10x \][/tex]
- Last terms: Multiply the last terms:
[tex]\[ -5 \times -7 = 35 \][/tex]
2. Combine like terms:
- For the [tex]\(x\)[/tex] terms, combine [tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]:
[tex]\[ -21x - 10x = -31x \][/tex]
3. Write the expanded expression:
By combining all the terms together, the expression becomes:
[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].
1. Apply the distributive property (also known as the FOIL method for binomials):
- First terms: Multiply the first terms from each binomial:
[tex]\[ 3x \times 2x = 6x^2 \][/tex]
- Outer terms: Multiply the outer terms:
[tex]\[ 3x \times -7 = -21x \][/tex]
- Inner terms: Multiply the inner terms:
[tex]\[ -5 \times 2x = -10x \][/tex]
- Last terms: Multiply the last terms:
[tex]\[ -5 \times -7 = 35 \][/tex]
2. Combine like terms:
- For the [tex]\(x\)[/tex] terms, combine [tex]\(-21x\)[/tex] and [tex]\(-10x\)[/tex]:
[tex]\[ -21x - 10x = -31x \][/tex]
3. Write the expanded expression:
By combining all the terms together, the expression becomes:
[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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