Pregunta
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The simplified form is \( a^2 - 4 \).
Solución
Calculate or simplify the expression \( \frac{-2(a-1)(a+2)(a-2)}{2(1-a)} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{-2\left(a-1\right)\left(a+2\right)\left(a-2\right)}{2\left(1-a\right)}\)
- step1: Reduce the fraction:
\(-\frac{2\left(a-1\right)\left(a+2\right)\left(a-2\right)}{2\left(1-a\right)}\)
- step2: Reduce the fraction:
\(-\frac{\left(a-1\right)\left(a+2\right)\left(a-2\right)}{1-a}\)
- step3: Rewrite the expression:
\(-\frac{\left(a-1\right)\left(a+2\right)\left(a-2\right)}{-a+1}\)
- step4: Use the rules for multiplication and division:
\(\frac{\left(a-1\right)\left(a+2\right)\left(a-2\right)}{a-1}\)
- step5: Reduce the fraction:
\(\left(a+2\right)\left(a-2\right)\)
- step6: Simplify the product:
\(a^{2}-2^{2}\)
- step7: Evaluate the power:
\(a^{2}-4\)
The simplified form of the given expression \( \frac{-2(a-1)(a+2)(a-2)}{2(1-a)} \) is \( a^2 - 4 \).
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución The Deep Dive
To simplify the expression \( \frac{-2(a-1)(a+2)(a-2)}{2(1-a)} \), notice that the numerator is \( -2(a-1)(a+2)(a-2) \) and the denominator is \( 2(1-a) \). First, simplify the fraction by canceling out the common factor of 2 in the numerator and denominator: \[ \frac{-2(a-1)(a+2)(a-2)}{2(1-a)} = \frac{-(a-1)(a+2)(a-2)}{1-a} \] Now, observe that \( 1-a = -(a-1) \). You can substitute this back into the expression: \[ \frac{-(a-1)(a+2)(a-2)}{-(a-1)} = (a+2)(a-2) \quad \text{for } a \neq 1 \] Thus, the final simplified expression is: \[ (a+2)(a-2) = a^2 - 4 \quad \text{for } a \neq 1 \]
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