Questions: Simplify. 5(4y-5)+4(3y+3)

Transcript text: Simplify. \[ 5(4 y-5)+4(3 y+3) \]

Solution

Solution Steps

To simplify the given expression, we need to apply the distributive property to both terms and then combine like terms. The distributive property involves multiplying each term inside the parentheses by the factor outside. After distributing, we will add or subtract the coefficients of like terms to simplify the expression.

Step 1: Distribute the Constants

First, we need to distribute the constants 5 and 4 into the terms inside the parentheses.

\[ 5(4y - 5) = 5 \cdot 4y - 5 \cdot 5 = 20y - 25 \]

\[ 4(3y + 3) = 4 \cdot 3y + 4 \cdot 3 = 12y + 12 \]

Step 2: Combine Like Terms

Now, we combine the like terms from the expressions we obtained in Step 1.

\[ 20y - 25 + 12y + 12 \]

Combine the \(y\) terms:

\[ 20y + 12y = 32y \]

Combine the constant terms:

\[ -25 + 12 = -13 \]