Answer :
To multiply the binomials [tex]\((5x + 2)(7x + 3)\)[/tex], let's go through the steps using the distributive property, also known as the FOIL method:
1. First: Multiply the first terms in each binomial:
[tex]\[
5x \times 7x = 35x^2
\][/tex]
2. Outer: Multiply the outer terms in the product:
[tex]\[
5x \times 3 = 15x
\][/tex]
3. Inner: Multiply the inner terms in the product:
[tex]\[
2 \times 7x = 14x
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
2 \times 3 = 6
\][/tex]
Next, we combine all these results into a single polynomial expression:
- The result from the first terms is [tex]\(35x^2\)[/tex].
- Add the results from the outer and inner terms to get the combined linear term:
[tex]\[
15x + 14x = 29x
\][/tex]
- The result from the last terms is [tex]\(6\)[/tex].
So, when you combine all these, the final product of [tex]\((5x + 2)(7x + 3)\)[/tex] is:
[tex]\[
35x^2 + 29x + 6
\][/tex]
Therefore, the correct answer is [tex]\(35x^2 + 29x + 6\)[/tex].
1. First: Multiply the first terms in each binomial:
[tex]\[
5x \times 7x = 35x^2
\][/tex]
2. Outer: Multiply the outer terms in the product:
[tex]\[
5x \times 3 = 15x
\][/tex]
3. Inner: Multiply the inner terms in the product:
[tex]\[
2 \times 7x = 14x
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
2 \times 3 = 6
\][/tex]
Next, we combine all these results into a single polynomial expression:
- The result from the first terms is [tex]\(35x^2\)[/tex].
- Add the results from the outer and inner terms to get the combined linear term:
[tex]\[
15x + 14x = 29x
\][/tex]
- The result from the last terms is [tex]\(6\)[/tex].
So, when you combine all these, the final product of [tex]\((5x + 2)(7x + 3)\)[/tex] is:
[tex]\[
35x^2 + 29x + 6
\][/tex]
Therefore, the correct answer is [tex]\(35x^2 + 29x + 6\)[/tex].
