Algebra Examples

${- 2, 2}$

$x = - 2$ and $x = 2$ are the two real distinct solutions for the quadratic equation, which means that $x + 2$ and $x - 2$ are the factors of the quadratic equation.

$(x + 2) (x - 2) = 0$

Expand $(x + 2) (x - 2)$ using the FOIL Method.

Tap for more steps...

Apply the distributive property.

$x (x - 2) + 2 (x - 2) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 2 + 2 (x - 2) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 2 + 2 x + 2 \cdot - 2 = 0$

Simplify terms.

Tap for more steps...

Combine the opposite terms in $x \cdot x + x \cdot - 2 + 2 x + 2 \cdot - 2$ .

Tap for more steps...

Reorder the factors in the terms $x \cdot - 2$ and $2 x$ .

$x \cdot x - 2 x + 2 x + 2 \cdot - 2 = 0$

Add $- 2 x$ and $2 x$ .

$x \cdot x + 0 + 2 \cdot - 2 = 0$

Add $x \cdot x$ and $0$ .

$x \cdot x + 2 \cdot - 2 = 0$

Simplify each term.

Tap for more steps...

Multiply $x$ by $x$ .

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

Multiply $2$ by $- 2$ .

$x^{2} - 4 = 0$

The standard quadratic equation using the given set of solutions ${- 2, 2}$ is $y = x^{2} - 4$ .

$y = x^{2} - 4$