Question

(2 points) Fill in the blanks with the correct coefficients when simplifying the expression. (10x+4y)+(7x+9y) x+ y

Answer 1

To simplify the expression \((10x + 4y) + (7x + 9y)(x + y)\), we first need to distribute \( (7x + 9y) \) across \( (x + y) \):

1. Distributing \( (7x + 9y) \) gives us:
\[
(7x + 9y)(x + y) = 7x \cdot x + 7x \cdot y + 9y \cdot x + 9y \cdot y
\]
This simplifies to:
\[
7x^2 + 7xy + 9xy + 9y^2 = 7x^2 + (7 + 9)xy + 9y^2 = 7x^2 + 16xy + 9y^2
\]

2. Now we combine this with \( (10x + 4y) \):
\[
(10x + 4y) + (7x^2 + 16xy + 9y^2) = 7x^2 + 10x + 16xy + 4y + 9y^2
\]

The final expression is:
\[
7x^2 + 10x + 16xy + 9y^2 + 4y
\]

The coefficients are:
- For \( x^2 \): **7**
- For \( xy \): **16**
- For \( x \): **10**
- For \( y^2 \): **9**
- For \( y \): **4**