To find the product of the expression [tex]\((y + 3)(5y + 1)\)[/tex], we can use the distributive property, sometimes referred to as the FOIL method (First, Outer, Inner, Last). Let's go through each step of the process.
1. First: Multiply the first terms in each binomial.
[tex]\[
y \cdot 5y = 5y^2
\][/tex]
2. Outer: Multiply the outer terms in each binomial.
[tex]\[
y \cdot 1 = y
\][/tex]
3. Inner: Multiply the inner terms in each binomial.
[tex]\[
3 \cdot 5y = 15y
\][/tex]
4. Last: Multiply the last terms in each binomial.
[tex]\[
3 \cdot 1 = 3
\][/tex]
Next, we add all these results together:
[tex]\[
5y^2 + y + 15y + 3
\][/tex]
Now, combine the like terms (the terms involving [tex]\(y\)[/tex]):
[tex]\[
y + 15y = 16y
\][/tex]
Therefore, the simplified expression is:
[tex]\[
5y^2 + 16y + 3
\][/tex]
So, the product of [tex]\((y+3)(5y+1)\)[/tex] simplified is:
[tex]\[
5y^2 + 16y + 3
\][/tex]
