Simplify Algebraic Expression: $5x - 2x(x - 1)$
To simplify the expression $5x - 2x(x - 1)$, follow these steps:
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Distribute: Apply the distributive property by multiplying $-2x$ by each term inside the parentheses $(x - 1)$.
- $(-2x) \times x = -2x^2$
- $(-2x) \times (-1) = +2x$
So, $-2x(x - 1)$ becomes $-2x^2 + 2x$.
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Substitute and Combine: Substitute the result back into the original expression and combine like terms.
- Original expression: $5x - 2x(x - 1)$
- Substitute: $5x + (-2x^2 + 2x)$
- Simplify: $5x - 2x^2 + 2x$
- Combine terms with $x$: $(5x + 2x) - 2x^2$
- Final simplified expression: $7x - 2x^2$
The simplified form of the expression $5x - 2x(x - 1)$ is $7x - 2x^2$. This corresponds to Option D.
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