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Answer :
To multiply the two binomials [tex]\((2x + 5)(3x - 7)\)[/tex], we will use the distributive property, also known as the FOIL method. FOIL stands for First, Outer, Inner, Last, which are the pairs of terms we need to multiply:
1. First: Multiply the first terms in each binomial:
[tex]\((2x) \times (3x) = 6x^2\)[/tex]
2. Outer: Multiply the outer terms in each binomial:
[tex]\((2x) \times (-7) = -14x\)[/tex]
3. Inner: Multiply the inner terms in each binomial:
[tex]\(5 \times (3x) = 15x\)[/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\(5 \times (-7) = -35\)[/tex]
Now, add all these products together:
[tex]\[6x^2 - 14x + 15x - 35\][/tex]
Next, combine the like terms:
The terms [tex]\(-14x\)[/tex] and [tex]\(15x\)[/tex] combine to [tex]\(1x\)[/tex] or simply [tex]\(x\)[/tex].
So, the resulting expression is:
[tex]\[6x^2 + x - 35\][/tex]
Therefore, the correct answer is:
C) [tex]\(6x^2 + x - 35\)[/tex]
1. First: Multiply the first terms in each binomial:
[tex]\((2x) \times (3x) = 6x^2\)[/tex]
2. Outer: Multiply the outer terms in each binomial:
[tex]\((2x) \times (-7) = -14x\)[/tex]
3. Inner: Multiply the inner terms in each binomial:
[tex]\(5 \times (3x) = 15x\)[/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\(5 \times (-7) = -35\)[/tex]
Now, add all these products together:
[tex]\[6x^2 - 14x + 15x - 35\][/tex]
Next, combine the like terms:
The terms [tex]\(-14x\)[/tex] and [tex]\(15x\)[/tex] combine to [tex]\(1x\)[/tex] or simply [tex]\(x\)[/tex].
So, the resulting expression is:
[tex]\[6x^2 + x - 35\][/tex]
Therefore, the correct answer is:
C) [tex]\(6x^2 + x - 35\)[/tex]
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