To simplify the expression \((10x + 4y) + (7x + 9y)(x + y)\), we first need to distribute \( (7x + 9y) \) across \( (x + y) \):
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Distributing \( (7x + 9y) \) gives us: \[ (7x + 9y)(x + y) = 7x \cdot x + 7x \cdot y + 9y \cdot x + 9y \cdot y \] This simplifies to: \[ 7x^2 + 7xy + 9xy + 9y^2 = 7x^2 + (7 + 9)xy + 9y^2 = 7x^2 + 16xy + 9y^2 \]
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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
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