Algebra Examples

${0, 1}$

$x = 0$ and $x = 1$ are the two real distinct solutions for the quadratic equation, which means that $x - 0$ and $x - 1$ are the factors of the quadratic equation.

$(x - 0) (x - 1) = 0$

Simplify by multiplying through.

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Subtract $0$ from $x$ .

$x (x - 1) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 1 = 0$

Simplify the expression.

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Multiply $x$ by $x$ .

$x^{2} + x \cdot - 1 = 0$

Move $- 1$ to the left of $x$ .

$x^{2} - 1 \cdot x = 0$

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x = 0$

The standard quadratic equation using the given set of solutions ${0, 1}$ is $y = x^{2} - x$ .

$y = x^{2} - x$