High School

Which of the following is the product of [tex]$(7x + 2)$[/tex] and [tex]$(5x - 11)$[/tex]?

A. [tex]$12x^2 - 10x - 77x - 22$[/tex]
B. [tex]$35x^2 - 67x - 22$[/tex]
C. [tex]$12x^2 - 67x - 22$[/tex]
D. [tex]$35x^2 + 67x + 22$[/tex]

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].