Answer :
To solve the expression [tex]\((3x - 5)(2x - 7)\)[/tex], we need to expand it using the distributive property, commonly referred to as the FOIL method (First, Outer, Inner, Last). Let's go through it step by step:
1. First: Multiply the first terms in each binomial.
- [tex]\(3x \times 2x = 6x^2\)[/tex]
2. Outer: Multiply the outer terms in the binomials.
- [tex]\(3x \times -7 = -21x\)[/tex]
3. Inner: Multiply the inner terms.
- [tex]\(-5 \times 2x = -10x\)[/tex]
4. Last: Multiply the last terms in each binomial.
- [tex]\(-5 \times -7 = 35\)[/tex]
Now, combine all these results together:
- The expression becomes [tex]\(6x^2 - 21x - 10x + 35\)[/tex].
Finally, combine like terms:
- Combine the [tex]\(x\)[/tex]-terms: [tex]\(-21x - 10x = -31x\)[/tex].
So, the expanded expression is:
[tex]\[6x^2 - 31x + 35\][/tex]
Therefore, the expression [tex]\((3x - 5)(2x - 7)\)[/tex] is equal to:
[tex]\[6x^2 - 31x + 35\][/tex]
Hence, the correct answer is [tex]\(6 x^2-31 x+35\)[/tex].
1. First: Multiply the first terms in each binomial.
- [tex]\(3x \times 2x = 6x^2\)[/tex]
2. Outer: Multiply the outer terms in the binomials.
- [tex]\(3x \times -7 = -21x\)[/tex]
3. Inner: Multiply the inner terms.
- [tex]\(-5 \times 2x = -10x\)[/tex]
4. Last: Multiply the last terms in each binomial.
- [tex]\(-5 \times -7 = 35\)[/tex]
Now, combine all these results together:
- The expression becomes [tex]\(6x^2 - 21x - 10x + 35\)[/tex].
Finally, combine like terms:
- Combine the [tex]\(x\)[/tex]-terms: [tex]\(-21x - 10x = -31x\)[/tex].
So, the expanded expression is:
[tex]\[6x^2 - 31x + 35\][/tex]
Therefore, the expression [tex]\((3x - 5)(2x - 7)\)[/tex] is equal to:
[tex]\[6x^2 - 31x + 35\][/tex]
Hence, the correct answer is [tex]\(6 x^2-31 x+35\)[/tex].
