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The simplified expression is \( \frac{1}{10}(x^2 - 146x - 61) \).
Solución
\[
\begin{aligned}
1.1\,(x-3)^2 - (x+4)^2 &= 1.1\,(x^2 - 6x + 9) - (x^2 + 8x + 16) \\
&= 1.1\,x^2 - 6.6\,x + 9.9 - x^2 - 8x - 16 \\
&= (1.1\,x^2 - x^2) + (-6.6\,x - 8x) + (9.9 - 16) \\
&= 0.1\,x^2 - 14.6\,x - 6.1.
\end{aligned}
\]
To write the answer in a more compact form, we can factor out \(0.1\) (which is equivalent to \(\frac{1}{10}\)):
\[
0.1\,x^2 - 14.6\,x - 6.1 = \frac{1}{10}\left( x^2 - 146\,x - 61 \right).
\]
Thus, the simplified expression is:
\[
\frac{1}{10}\left( x^2 - 146\,x - 61 \right).
\]
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución Mind Expander
To simplify the expression \( (x-3)^{2} - (x+4)^{2} \), we can use the difference of squares factorization. The difference of squares is defined as \( a^2 - b^2 = (a - b)(a + b) \). Here, let \( a = (x-3) \) and \( b = (x+4) \). Then, our expression becomes: \[ ((x-3) - (x+4))((x-3) + (x+4)) \] Now, simplify each part: 1. \( (x-3) - (x+4) = x - 3 - x - 4 = -7 \) 2. \( (x-3) + (x+4) = x - 3 + x + 4 = 2x + 1 \) Putting it all together, we have: \[ -7(2x + 1) \] Distributing the -7: \[ -14x - 7 \] So, the simplified expression is: \[ -14x - 7 \]
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