(2 points) Fill in the blanks with the correct coefficients when simplifying the expression. (14x+6y)+(5x+12y) x+ y

Answer 1

To simplify the expression \((14x + 6y) + (5x + 12y)\), we will first combine the like terms.

1. Combine the \(x\) terms:

   • \(14x + 5x = 19x\)

2. Combine the \(y\) terms:

   • \(6y + 12y = 18y\)

Now, putting it all together, we have: \[ 19x + 18y \]

Now, if you want to multiply the entire expression by \(x + y\), distribute it as follows:

\[ (19x + 18y)(x + y) \]

This gives:

1. \(19x \cdot x = 19x^2\)
2. \(19x \cdot y = 19xy\)
3. \(18y \cdot x = 18xy\)
4. \(18y \cdot y = 18y^2\)

Now combine the terms: \[ 19x^2 + (19xy + 18xy) + 18y^2 = 19x^2 + 37xy + 18y^2 \]

Thus, the final answer after simplifying is: \[ 19x^2 + 37xy + 18y^2 \]

To summarize, the coefficients are:

• For \(x^2\): 19
• For \(xy\): 37
• For \(y^2\): 18