Answer :
To multiply [tex]\((5x + 2)(7x + 3)\)[/tex], we can use the distributive property, also known as the FOIL method, which stands for First, Outer, Inner, and Last. Here's how you can do it step by step:
1. First: Multiply the first terms of each binomial:
[tex]\[
5x \cdot 7x = 35x^2
\][/tex]
2. Outer: Multiply the outer terms:
[tex]\[
5x \cdot 3 = 15x
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
2 \cdot 7x = 14x
\][/tex]
4. Last: Multiply the last terms of each binomial:
[tex]\[
2 \cdot 3 = 6
\][/tex]
5. Combine like terms: Add all these results together:
[tex]\[
35x^2 + 15x + 14x + 6
\][/tex]
6. Simplify: Combine the like terms [tex]\(15x\)[/tex] and [tex]\(14x\)[/tex]:
[tex]\[
35x^2 + (15x + 14x) + 6 = 35x^2 + 29x + 6
\][/tex]
So, the product of [tex]\((5x + 2)(7x + 3)\)[/tex] is [tex]\(\boxed{35x^2 + 29x + 6}\)[/tex].
1. First: Multiply the first terms of each binomial:
[tex]\[
5x \cdot 7x = 35x^2
\][/tex]
2. Outer: Multiply the outer terms:
[tex]\[
5x \cdot 3 = 15x
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
2 \cdot 7x = 14x
\][/tex]
4. Last: Multiply the last terms of each binomial:
[tex]\[
2 \cdot 3 = 6
\][/tex]
5. Combine like terms: Add all these results together:
[tex]\[
35x^2 + 15x + 14x + 6
\][/tex]
6. Simplify: Combine the like terms [tex]\(15x\)[/tex] and [tex]\(14x\)[/tex]:
[tex]\[
35x^2 + (15x + 14x) + 6 = 35x^2 + 29x + 6
\][/tex]
So, the product of [tex]\((5x + 2)(7x + 3)\)[/tex] is [tex]\(\boxed{35x^2 + 29x + 6}\)[/tex].
