Question

(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**