Let's simplify both expressions step by step.
First expression: \((3x+4x)+2x(3x+4x)+2x\)
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Simplify \(3x + 4x\): \[ 3x + 4x = 7x \] So, the expression becomes: \[ 7x + 2x(7x) + 2x \]
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Expand \(2x(7x)\): \[ 2x \cdot 7x = 14x^2 \] Now, the expression is: \[ 7x + 14x^2 + 2x \]
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Combine like terms \(7x + 2x\): \[ 7x + 2x = 9x \] Thus, the first expression simplifies to: \[ 14x^2 + 9x \]
Second expression: \(3x+(4x+2x)3x+(4x+2x)\)
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Simplify \(4x + 2x\): \[ 4x + 2x = 6x \] So, the expression becomes: \[ 3x + (6x)(3x) + 6x \]
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Expand \((6x)(3x)\): \[ 6x \cdot 3x = 18x^2 \] Now, the expression is: \[ 3x + 18x^2 + 6x \]
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Combine like terms \(3x + 6x\): \[ 3x + 6x = 9x \] Thus, the second expression simplifies to: \[ 18x^2 + 9x \]
Comparing Both Expressions:
- First expression: \(14x^2 + 9x\)
- Second expression: \(18x^2 + 9x\)
To find the difference: \[ (14x^2 + 9x) - (18x^2 + 9x) = 14x^2 + 9x - 18x^2 - 9x \] The \(9x\) terms cancel out: \[ 14x^2 - 18x^2 = -4x^2 \]
Thus, the difference between the two expressions is: \[ \boxed{-4x^2} \]