Answer :
To solve the expression [tex]\((3x - 7)(3x - 5)\)[/tex], we need to expand it using the distributive property. This method is sometimes referred to as the FOIL method, which stands for First, Outer, Inner, Last, and helps organize the multiplication process. Let's break it down step by step:
1. First: Multiply the first terms in each binomial.
- [tex]\(3x \times 3x = 9x^2\)[/tex]
2. Outer: Multiply the outer terms in the expression.
- [tex]\(3x \times -5 = -15x\)[/tex]
3. Inner: Multiply the inner terms.
- [tex]\(-7 \times 3x = -21x\)[/tex]
4. Last: Multiply the last terms in each binomial.
- [tex]\(-7 \times -5 = 35\)[/tex]
Next, we need to combine the like terms:
- Combine the terms with [tex]\(x\)[/tex]: [tex]\(-15x - 21x = -36x\)[/tex]
After combining, the expanded expression becomes:
[tex]\[9x^2 - 36x + 35\][/tex]
Thus, the expanded form of [tex]\((3x - 7)(3x - 5)\)[/tex] is [tex]\(9x^2 - 36x + 35\)[/tex]. So, the correct answer is not listed among the given choices.
1. First: Multiply the first terms in each binomial.
- [tex]\(3x \times 3x = 9x^2\)[/tex]
2. Outer: Multiply the outer terms in the expression.
- [tex]\(3x \times -5 = -15x\)[/tex]
3. Inner: Multiply the inner terms.
- [tex]\(-7 \times 3x = -21x\)[/tex]
4. Last: Multiply the last terms in each binomial.
- [tex]\(-7 \times -5 = 35\)[/tex]
Next, we need to combine the like terms:
- Combine the terms with [tex]\(x\)[/tex]: [tex]\(-15x - 21x = -36x\)[/tex]
After combining, the expanded expression becomes:
[tex]\[9x^2 - 36x + 35\][/tex]
Thus, the expanded form of [tex]\((3x - 7)(3x - 5)\)[/tex] is [tex]\(9x^2 - 36x + 35\)[/tex]. So, the correct answer is not listed among the given choices.
