Questions: 5x^2-7(x+2)^2+4x-2

5x^2-7(x+2)^2+4x-2
Transcript text: d) $5 x^{2}-7(x+2)^{2}+4 x-2$
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Solution

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Solution Steps

Step 1: Expand the Expression

We start with the expression \( 5x^{2} - 7(x+2)^{2} + 4x - 2 \). First, we expand the squared term \( (x+2)^{2} \): \[ (x+2)^{2} = x^{2} + 4x + 4 \] Substituting this back into the expression gives: \[ 5x^{2} - 7(x^{2} + 4x + 4) + 4x - 2 \]

Step 2: Distribute and Combine Like Terms

Next, we distribute \(-7\) across the expanded terms: \[ 5x^{2} - 7x^{2} - 28x - 28 + 4x - 2 \] Now, we combine the like terms: \[ (5x^{2} - 7x^{2}) + (-28x + 4x) + (-28 - 2) = -2x^{2} - 24x - 30 \]

Final Answer

The simplified expression is: \[ \boxed{-2x^{2} - 24x - 30} \]

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