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Answer :
To find the product of the expressions [tex]\((7x + 2)\)[/tex] and [tex]\((5x - 11)\)[/tex], we can use the distributive property, also known as the FOIL method (First, Outer, Inner, Last) for multiplying two binomials. Here's how you can do it step-by-step:
1. First: Multiply the first terms in each binomial:
[tex]\[
7x \cdot 5x = 35x^2
\][/tex]
2. Outer: Multiply the outer terms in the parentheses:
[tex]\[
7x \cdot (-11) = -77x
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
2 \cdot 5x = 10x
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
2 \cdot (-11) = -22
\][/tex]
Now, combine all these results to get the expanded polynomial:
[tex]\[
35x^2 - 77x + 10x - 22
\][/tex]
Next, combine the like terms, which are the [tex]\(x\)[/tex] terms:
[tex]\[
-77x + 10x = -67x
\][/tex]
Finally, write down the combined polynomial:
[tex]\[
35x^2 - 67x - 22
\][/tex]
So, the product of [tex]\((7x + 2)\)[/tex] and [tex]\((5x - 11)\)[/tex] is:
[tex]\[
35x^2 - 67x - 22
\][/tex]
The correct choice from the given options is B. [tex]\(35x^2 - 67x - 22\)[/tex].
1. First: Multiply the first terms in each binomial:
[tex]\[
7x \cdot 5x = 35x^2
\][/tex]
2. Outer: Multiply the outer terms in the parentheses:
[tex]\[
7x \cdot (-11) = -77x
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
2 \cdot 5x = 10x
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
2 \cdot (-11) = -22
\][/tex]
Now, combine all these results to get the expanded polynomial:
[tex]\[
35x^2 - 77x + 10x - 22
\][/tex]
Next, combine the like terms, which are the [tex]\(x\)[/tex] terms:
[tex]\[
-77x + 10x = -67x
\][/tex]
Finally, write down the combined polynomial:
[tex]\[
35x^2 - 67x - 22
\][/tex]
So, the product of [tex]\((7x + 2)\)[/tex] and [tex]\((5x - 11)\)[/tex] is:
[tex]\[
35x^2 - 67x - 22
\][/tex]
The correct choice from the given options is B. [tex]\(35x^2 - 67x - 22\)[/tex].
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