Question

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

Answer 1

To simplify the expression \((18x + 9y) + (2x + 6y)(x + y)\), we first need to distribute the second part.

1. **Distributing \((2x + 6y)\) with \((x + y)\)**:
\[
(2x + 6y)(x + y) = 2x \cdot x + 2x \cdot y + 6y \cdot x + 6y \cdot y
\]
Simplifying this gives:
\[
= 2x^2 + 2xy + 6xy + 6y^2
\]
Combining the like terms \(2xy\) and \(6xy\) results in:
\[
= 2x^2 + 8xy + 6y^2
\]

2. **Now combine this with \((18x + 9y)\)**:
\[
(18x + 9y) + (2x^2 + 8xy + 6y^2)
\]
Rearranging and combining the like terms:
- The \(x^2\) term is \(2x^2\).
- The \(xy\) terms are \(8xy\).
- The \(y\) term is \(9y\) and the \(x\) terms are \(18x\).

Combine all components:
\[
= 2x^2 + 18x + 8xy + 9y + 6y^2
\]

Throughout this simplification, the coefficients for each term remain:
- Coefficient of \(x^2\) is **2**,
- Coefficient of \(x\) is **18**,
- Coefficient of \(xy\) is **8**,
- Coefficient of \(y\) is **9**,
- Coefficient of \(y^2\) is **6**.

Thus, the coefficients you are looking to fill in for the expression are:
- For \(x^2\): **2**
- For \(x\): **18**
- For \(xy\): **8**
- For \(y\): **9**
- For \(y^2\): **6**