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The simplified form is \(-14x - 7\).
Solución
Calculate or simplify the expression \( (x-3)^{2}-(x+4)^{2} \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(x-3\right)^{2}-\left(x+4\right)^{2}\)
- step1: Expand the expression:
\(x^{2}-6x+9-\left(x+4\right)^{2}\)
- step2: Expand the expression:
\(x^{2}-6x+9-x^{2}-8x-16\)
- step3: Collect like terms:
\(-14x-7\)
The simplified form of the expression \((x-3)^{2}-(x+4)^{2}\) is \(-14x-7\).
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Simplifique esta solución Bonus Knowledge
To simplify the expression \( (x-3)^{2} - (x+4)^{2} \), we can use the difference of squares formula, which states that \( a^2 - b^2 = (a-b)(a+b) \). Here, let's denote: - \( a = x - 3 \) - \( b = x + 4 \) Now, we have: \[ (x-3)^{2} - (x+4)^{2} = ( (x-3) - (x+4) )((x-3) + (x+4)) \] Calculating \( (x-3) - (x+4) \): \[ (x - 3) - (x + 4) = x - 3 - x - 4 = -7 \] Calculating \( (x-3) + (x+4) \): \[ (x - 3) + (x + 4) = x - 3 + x + 4 = 2x + 1 \] Putting it all together, we substitute back: \[ (x-3)^{2} - (x+4)^{2} = (-7)(2x + 1) \] Now, simply multiply this out: \[ = -14x - 7 \] Thus, the simplified expression is: \[ \boxed{-14x - 7} \]
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