To simplify the expression \((10x + 4y) + (7x + 9y)(x + y)\), we need to distribute and combine like terms.
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First, simplify \((7x + 9y)(x + y)\):
- Using the distributive property (or FOIL method): \[ (7x + 9y)(x + y) = 7x \cdot x + 7x \cdot y + 9y \cdot x + 9y \cdot y = 7x^2 + 7xy + 9xy + 9y^2 \]
- Combine like terms: \[ = 7x^2 + (7 + 9)xy + 9y^2 = 7x^2 + 16xy + 9y^2 \]
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Now, add this result to \((10x + 4y)\): \[ (10x + 4y) + (7x^2 + 16xy + 9y^2) = 7x^2 + 10x + 16xy + 4y + 9y^2 \]
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Combining the components leads to: \[ 7x^2 + 10x + 16xy + 4y + 9y^2 \]
Thus, the coefficients of the simplified expression are:
- Coefficient of \(x^2\): 7
- Coefficient of \(x\): 10
- Coefficient of \(xy\): 16
- Coefficient of \(y\): 4
- Coefficient of \(y^2\): 9
So the final simplification yields: \[ \text{Expression: } 7x^2 + 10x + 16xy + 4y + 9y^2 \]