Answer :
To find the product of the expressions [tex]\((7x + 2)\)[/tex] and [tex]\((5x - 11)\)[/tex], we can use the distributive property, which is often remembered as the FOIL method (First, Outer, Inner, Last). Let's break it down step by step:
1. First: Multiply the first terms of each binomial:
[tex]\[
7x \cdot 5x = 35x^2
\][/tex]
2. Outer: Multiply the outer terms:
[tex]\[
7x \cdot (-11) = -77x
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
2 \cdot 5x = 10x
\][/tex]
4. Last: Multiply the last terms of each binomial:
[tex]\[
2 \cdot (-11) = -22
\][/tex]
Next, we combine the like terms from these products:
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-77x\)[/tex] and [tex]\(10x\)[/tex]:
[tex]\[
-77x + 10x = -67x
\][/tex]
Finally, construct the polynomial from the combined terms:
- The [tex]\(x^2\)[/tex] term: [tex]\(35x^2\)[/tex]
- The combined [tex]\(x\)[/tex] terms: [tex]\(-67x\)[/tex]
- The constant term: [tex]\(-22\)[/tex]
Thus, the product of [tex]\((7x + 2)\)[/tex] and [tex]\((5x - 11)\)[/tex] is:
[tex]\[
35x^2 - 67x - 22
\][/tex]
So, the correct answer is B: [tex]\(35x^2 - 67x - 22\)[/tex].
1. First: Multiply the first terms of each binomial:
[tex]\[
7x \cdot 5x = 35x^2
\][/tex]
2. Outer: Multiply the outer terms:
[tex]\[
7x \cdot (-11) = -77x
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
2 \cdot 5x = 10x
\][/tex]
4. Last: Multiply the last terms of each binomial:
[tex]\[
2 \cdot (-11) = -22
\][/tex]
Next, we combine the like terms from these products:
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-77x\)[/tex] and [tex]\(10x\)[/tex]:
[tex]\[
-77x + 10x = -67x
\][/tex]
Finally, construct the polynomial from the combined terms:
- The [tex]\(x^2\)[/tex] term: [tex]\(35x^2\)[/tex]
- The combined [tex]\(x\)[/tex] terms: [tex]\(-67x\)[/tex]
- The constant term: [tex]\(-22\)[/tex]
Thus, the product of [tex]\((7x + 2)\)[/tex] and [tex]\((5x - 11)\)[/tex] is:
[tex]\[
35x^2 - 67x - 22
\][/tex]
So, the correct answer is B: [tex]\(35x^2 - 67x - 22\)[/tex].
