Algebra Examples

$4$ , $- 4$

Step 1

$x = 4$ and $x = - 4$ are the two real distinct solutions for the quadratic equation, which means that $x - 4$ and $x + 4$ are the factors of the quadratic equation.

$(x - 4) (x + 4) = 0$

Step 2

Expand $(x - 4) (x + 4)$ using the FOIL Method.

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Apply the distributive property.

$x (x + 4) - 4 (x + 4) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 4 - 4 (x + 4) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 4 - 4 x - 4 \cdot 4 = 0$

Step 3

Simplify terms.

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Combine the opposite terms in $x \cdot x + x \cdot 4 - 4 x - 4 \cdot 4$ .

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Reorder the factors in the terms $x \cdot 4$ and $- 4 x$ .

$x \cdot x + 4 x - 4 x - 4 \cdot 4 = 0$

Subtract $4 x$ from $4 x$ .

$x \cdot x + 0 - 4 \cdot 4 = 0$

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

$x \cdot x - 4 \cdot 4 = 0$

Simplify each term.

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Multiply $x$ by $x$ .

$x^{2} - 4 \cdot 4 = 0$

Multiply $- 4$ by $4$ .

$x^{2} - 16 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${4, - 4}$ is $y = x^{2} - 16$ .

$y = x^{2} - 16$

Step 5