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Simplify the expression: y = x + 2(1/3x2 + 1/3x + 1/3)

April 19, 2026Mathematics

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Answer

y = \frac{2}{3}x^2 + \frac{5}{3}x + \frac{2}{3}

Graph of y = x + 2(1/3x² + 1/3x + 1/3)

2 steps

Distribute the 2 into the terms inside the parenthesis.
$y = x + 2\left(\frac{1}{3}x^2\right) + 2\left(\frac{1}{3}x\right) + 2\left(\frac{1}{3}\right)$ $y = x + \frac{2}{3}x^2 + \frac{2}{3}x + \frac{2}{3}$
Combine the like terms.
The terms with $x$ are $x$ and $\frac{2}{3}x$ .
$y = \frac{2}{3}x^2 + \left(1 + \frac{2}{3}\right)x + \frac{2}{3}$ $y = \frac{2}{3}x^2 + \left(\frac{3}{3} + \frac{2}{3}\right)x + \frac{2}{3}$ $y = \frac{2}{3}x^2 + \frac{5}{3}x + \frac{2}{3}$

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