Let's simplify the expression \( y(6y + 2) + 5(2y + 4) \):

### Step 1: Distribute \( y \) and \( 5 \) to each term inside their respective parentheses.

1. \( y(6y + 2) = 6y^2 + 2y \)
2. \( 5(2y + 4) = 10y + 20 \)

### Step 2: Combine the two expanded parts.

Now, add the two parts together:
\[
6y^2 + 2y + 10y + 20
\]

### Step 3: Combine like terms.

\[
6y^2 + (2y + 10y) + 20 = 6y^2 + 12y + 20
\]

Thus, the simplified expression is:
\[
6y^2 + 12y + 20
\]

Would you like a further breakdown or have any questions?

Here are 5 related questions to expand on this:
1. How do you factor the expression \( 6y^2 + 12y + 20 \)?
2. What is the value of the expression if \( y = 1 \)?
3. Can you solve \( 6y^2 + 12y + 20 = 0 \) using the quadratic formula?
4. What is the degree of the polynomial \( 6y^2 + 12y + 20 \)?
5. How do you identify the leading coefficient of a quadratic expression?

**Tip:** Always look for like terms in an expression to combine them and simplify!

Learn how to simplify the algebraic expression y(6y + 2) + 5(2y + 4) using the distributive property. This problem covers key concepts in algebra, such as polynomial expansion and combining like terms. Suitable for students in Grades 7-9.

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