Subjects algebra

Expression Simplification

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Expression Simplification


1. **State the problem:** Simplify or rearrange the expression $y - 6x + 2xy - 3$. 2. **Group like terms:** There are terms with $y$, terms with $x$, and constants. The terms are $y$, $-6x$, $2xy$, and $-3$. 3. **Check if any factorization or simplification is possible:** The expression has $y$ and $2xy$ which involve $y$. We can factor $y$ from these terms: $$y + 2xy = y(1 + 2x)$$ 4. **Rewrite the whole expression:** $$y(1 + 2x) - 6x - 3$$ 5. **Interpretation:** The expression can be viewed as $y(1 + 2x)$ minus terms $6x$ and $3$. There are no like terms to combine further. **Final simplified form:** $$y(1 + 2x) - 6x - 3$$