Question

(2 points) Fill in the blanks with the correct coefficients when simplifying the expression. (18x+9y)+(2x+6y) x+ y

Answer 1

To simplify the expression \((18x + 9y) + (2x + 6y) \cdot (x + y)\), we need to break it down step by step:

1. First, we calculate the multiplication \((2x + 6y) \cdot (x + y)\):

- Distributing \(2x\):
\[
2x \cdot x + 2x \cdot y = 2x^2 + 2xy
\]

- Distributing \(6y\):
\[
6y \cdot x + 6y \cdot y = 6xy + 6y^2
\]

Now combine these results:
\[
(2x + 6y) \cdot (x + y) = 2x^2 + 2xy + 6xy + 6y^2 = 2x^2 + 8xy + 6y^2
\]

2. Next, we combine this result with the first part of the expression:
\[
(18x + 9y) + (2x^2 + 8xy + 6y^2)
\]

Combining like terms:
- The \(x^2\) term: \(2x^2\)
- The \(xy\) terms: \(8xy\)
- The \(x\) terms: \(18x\)
- The \(y\) terms: \(9y + 6y^2\) since we only have the constant \(y\) term.

So, the final simplified expression is:
\[
2x^2 + 18x + 8xy + 9y + 6y^2
\]

Thus, the coefficients to fill the blanks, if asked for in the final polynomial, are:

- Coefficient of \(x^2\): 2
- Coefficient of \(xy\): 8
- Coefficient of \(x\): 18
- Coefficient of \(y\): 9
- Coefficient of \(y^2\): 6

Please confirm the specific blanks you wanted to fill if this is not what you were looking for!