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Answer :
To find the product of [tex]\((7x + 2)\)[/tex] and [tex]\((5x - 11)\)[/tex], we can use the distributive property, often remembered as the FOIL method for multiplying binomials. Let's go through the steps:
1. First terms: Multiply the first terms in each binomial:
[tex]\[
7x \times 5x = 35x^2
\][/tex]
2. Outer terms: Multiply the outer terms:
[tex]\[
7x \times -11 = -77x
\][/tex]
3. Inner terms: Multiply the inner terms:
[tex]\[
2 \times 5x = 10x
\][/tex]
4. Last terms: Multiply the last terms:
[tex]\[
2 \times -11 = -22
\][/tex]
Now, combine all these results:
[tex]\[
35x^2 - 77x + 10x - 22
\][/tex]
Combine the like terms, which are the middle terms [tex]\(-77x\)[/tex] and [tex]\(10x\)[/tex]:
[tex]\[
35x^2 - 67x - 22
\][/tex]
So, the product of [tex]\((7x + 2)\)[/tex] and [tex]\((5x - 11)\)[/tex] is:
[tex]\[
\boxed{35x^2 - 67x - 22}
\][/tex]
The correct choice is (B) [tex]\(35x^2 - 67x - 22\)[/tex].
1. First terms: Multiply the first terms in each binomial:
[tex]\[
7x \times 5x = 35x^2
\][/tex]
2. Outer terms: Multiply the outer terms:
[tex]\[
7x \times -11 = -77x
\][/tex]
3. Inner terms: Multiply the inner terms:
[tex]\[
2 \times 5x = 10x
\][/tex]
4. Last terms: Multiply the last terms:
[tex]\[
2 \times -11 = -22
\][/tex]
Now, combine all these results:
[tex]\[
35x^2 - 77x + 10x - 22
\][/tex]
Combine the like terms, which are the middle terms [tex]\(-77x\)[/tex] and [tex]\(10x\)[/tex]:
[tex]\[
35x^2 - 67x - 22
\][/tex]
So, the product of [tex]\((7x + 2)\)[/tex] and [tex]\((5x - 11)\)[/tex] is:
[tex]\[
\boxed{35x^2 - 67x - 22}
\][/tex]
The correct choice is (B) [tex]\(35x^2 - 67x - 22\)[/tex].
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