Pregunta
11. \( \left(\frac{x}{3}-2\right)\left(\frac{x}{2}-3\right) \)
Ask by Vaughn Gibson. in South Africa
Mar 17,2025
Solución de inteligencia artificial de Upstudy
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The expression simplifies to \( \frac{x^{2}-12x+36}{6} \).
Solución
Calculate or simplify the expression \( (x/3-2)*(x/2-3) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(\frac{x}{3}-2\right)\left(\frac{x}{2}-3\right)\)
- step1: Subtract the terms:
\(\frac{x-6}{3}\times \left(\frac{x}{2}-3\right)\)
- step2: Subtract the terms:
\(\frac{x-6}{3}\times \frac{x-6}{2}\)
- step3: Multiply the terms:
\(\frac{\left(x-6\right)\left(x-6\right)}{3\times 2}\)
- step4: Multiply the terms:
\(\frac{\left(x-6\right)^{2}}{3\times 2}\)
- step5: Multiply the terms:
\(\frac{\left(x-6\right)^{2}}{6}\)
- step6: Calculate:
\(\frac{x^{2}-12x+36}{6}\)
The expression \( \left(\frac{x}{3}-2\right)\left(\frac{x}{2}-3\right) \) simplifies to \( \frac{x^{2}-12x+36}{6} \).
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Simplifique esta solución Beyond the Answer
Did you know that expanding expressions like \( \left(\frac{x}{3}-2\right)\left(\frac{x}{2}-3\right) \) can be a fun way to explore algebraic relationships? By applying the distributive property, also known as the FOIL method for binomials, you can reveal how the components work together. Multiply the first terms, the outer terms, the inner terms, and the last terms to get a complete expression. Once expanded, the expression becomes \( \frac{x^2}{6} - \frac{11x}{3} + 6 \). This shows how you can take a complex-looking factorization and transform it into a standard polynomial form. It's like peeling back the layers of an onion to see what's inside!
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